Yuchen Xie, Baoming Shi, Yucen Han +1cond-mat.soft cs.LG
Smectic liquid crystals are layered liquid-crystalline phases characterized by orientational order and periodic density modulation. Although their structures can be modeled using continuum theories, computing stable configurations remains challenging in complex geometries, particularly when the high-frequency density modulations associated with smectic layering should be resolved. We propose a deep variational framework (DVF) for computing these configurations within the modified Landau--de Gennes model, in which the coupled orientational and positional order parameters are represented on a regular reference domain while physical confinement is incorporated through coordinate mappings. A warmup penalty mitigates the spectral bias of neural networks toward smooth, nonlayered fields, enabling robust recovery of oscillatory smectic states. Comparisons with a neural-network baseline and finite-difference relaxation demonstrate the essential role of this penalty and the numerical stability of the resulting layered states. The DVF reproduces experimentally established smectic-A defect structures and layer morphologies across diverse confinement geometries and further predicts a chevron-like smectic-C state in a tangent-anchored sphere. Together, these results demonstrate the applicability of the DVF to computing stable smectic configurations across experimentally relevant confinement geometries and anchoring conditions.
Lidia J. Gomes Da Silvagr-qc astro-ph.HE astro-ph.IM cs.LG physics.comp-ph
Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.
Leonid Popryho, Ayoub Sadeghi, Inna Partin-Vaisbandcs.LG cs.AR cs.CE
High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.
Magnetic core loss originates in the hysteresis loop: the energy dissipated per excitation cycle equals the loop area, and frequency, temperature, and waveform shape set the loss by reshaping the loop geometry. Most existing models let these conditions act only on a terminal scalar - empirical equations fold them into fitted exponents, and data-driven predictors append them to encoded features - so no intermediate hysteresis representation remains for the conditions to reshape. This paper proposes CAHR-Net, a condition-adaptive hysteresis reconstruction network that injects the operating conditions where they physically act. It preserves the interpretable chain from flux density waveform to magnetic field reconstruction, loop-area integration, and power loss estimation, and uses feature-wise linear modulation to inject frequency, temperature, and waveform statistics into the intermediate reconstruction representation. A matched large-batch training protocol based on AdamW, cosine scheduling, and a staged reconstruction-to-power-loss objective is also reported, because the modulation pathway takes effect only within it. On the MagNet final A-E material protocol, CAHR-Net attains an average p95 relative error of 6.89% with only 1874 parameters, the lowest among all compared methods, together with a lower worst-material p95 than the strongest black-box solution at about 48x fewer parameters; it reduces the average p95 of the physical reconstruction backbone from 7.47% to 6.89% and the p95 of material D, the most difficult material, from 16.40% to 14.87%. Ablation and condition-slice analyses attribute the improvement to the coupling of physical loop reconstruction, structured condition modulation, and the matched optimization trajectory.
Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at https://github.com/JingXiao10/GUA.
Sara Sameer, Yunyi Zhao, Wei Zhang +4cs.LG eess.SY
Battery health prognostics is a core function in battery management systems (BMSs), yet long-horizon health forecasting from BMS signals remains challenging due to operating-condition dependency and sensor noise. In this paper, we propose PhyMamba, a two-stage physics-modulated Mamba framework that integrates electrochemical aging into sequence modelling. PhyMamba does not require explicit identification of internal aging parameters, which often relies on intrusive measurements. In stage-1, a lightweight Mamba encoder first processes BMS signals and produces a latent representation that is transformed via an aging parameterization module, into physics-informed aging features. In stage-2, a customized Mamba forecasting backbone performs multi-cycle prediction, where physics is tightly integrated to regulate the model's internal temporal updates toward degradation-consistent evolution. Experiments on three public datasets under multiple forecast horizons show that PhyMamba achieves the best aggregated performance, with an overall mean error reduction of 31.8% compared with a diverse range of baselines. PhyMamba also offers an optimized accuracy-efficiency trade-off, which supports practical deployment for robust battery health prognostics.
Deep generative models such as flow matching and diffusion models have shown potential for learning complex dynamical systems, but typically act as black boxes that neglect underlying physical structure, while physics-based models governed by partial differential equations are often incomplete due to missing source terms, or uncertain parametrisations. We present Climate Physics Dynamic Matching (ClimPhyDM), a variational simulation-free dynamics informed framework for weather forecasting that combines an advection-type physics prior with data-driven components in a variational framework. % to capture the stochasticity and multi-modality of unresolved atmospheric dynamics. On the ERA5 benchmark at hourly (42-hour) and monthly (5-month) resolutions, ClimPhyDM outperforms ClimODE, and GB-DM, keeping the lower error at extended horizon, indicating improved temporal stability and resistance to error accumulation, while its simulation-free paradigm also enables training on a single modest 12 GB consumer GPU.
While Physics-Informed Neural Networks (PINNs) have emerged as a transformative paradigm for solving complex differential equations, their reliance on backpropagation-based gradient descent and automatic differentiation (AD) imposes significant computational bottlenecks and severe non-convex optimization challenges. To overcome these fundamental limitations, we propose the Physics-Informed Stochastic Configuration Machine (PI-SCM), a novel backpropagation-free framework for both forward and inverse problems in differential equations. The core mathematical contribution lies in the analytical evaluation of local Jacobians for nonlinear differential operators, which facilitates a linearized representation of the physical loss and projects it into a unified, linearized algebraic subspace. This reformulation allows for the explicit determination of optimal network weights via a sequence of generalized linear least squares solvers, effectively bypassing the iterative traps of traditional nonlinear optimizers. We develop a progressive algorithmic suite comprising localized construction (PI-SC-I), sliding-window updating (PI-SC-II), and global updating (PI-SC-III), and rigorously establish their universal approximation properties. Extensive experiments demonstrate that PI-SCM achieves high-fidelity predictive accuracy and robust parameter identification while accelerating the training process by orders of magnitude compared to standard PINNs. Our work provides a highly efficient and scalable foundation for next-generation, real-time Scientific Machine Learning applications.
We address the simultaneous prediction of multiple high-dimensional physical fields governed by linear equality constraints, a setting that arises in many real-world applications in physics machine learning. Gaussian process (GP) regression is a widely used surrogate modeling approach due to its effectiveness in small-sample regimes and its ability to provide uncertainty quantification. However, applying GP models in this setting raises two major challenges: the high dimensionality of the discretized output fields and the enforcement of the physical constraint in predictions. For the latter, a common strategy consists in deducing one output from the others via the constraint relation. Through a benchmark, we show that this deductive approach is sensitive to the arbitrary choice of which output to deduce, affecting both predictive accuracy and uncertainty quantification. Consequently, there is a need for an approach that treats all fields symmetrically while strictly respecting the underlying physics. Motivated by these limitations, we propose a robust framework for jointly modeling constrained multi-field data. Our approach first leverages a specific PCA procedure for multi-field data, coined row-wise PCA, which has the interesting property of preserving the constraint in the latent space. Since standard PCA strategies for multi-field data do not preserve such constraints, we investigate theoretically the optimality of the row-wise choice. In a second step, we consider a linearly-constrained multi-output GP approach based on a specific kernel parametrization which is trained on the latent space of row-wise PCA. The proposed framework is validated on a population dynamics problem and on an industrial CFD application, which involves the prediction of Reynolds stress tensor components under the incompressibility constraint.
Wyatt A. Smith, Arkaitz Rodas, Marius D. Thomas +5hep-ph cs.LG nucl-th
Reconstructing scattering amplitudes from finite, noisy, and mutually inconsistent measurements is an ill-posed inverse problem common to many reactions relevant to particle physics. We introduce S-matrix informed neural networks (SINNs), and demonstrate their ability to learn scattering amplitudes directly from data while respecting first principles. We further develop a novel data selection procedure, which uses the response of constrained neural network ensembles to identify a set of experiments compatible with first principles, and with each other. We apply this framework to $ππ$ scattering, producing reusable amplitudes and correlated uncertainties without relying on a fixed functional form. We validate our results against residual model dependencies and training biases through closure tests and ablations. We find negligible impact of model architecture on our results. Our workflow unifies physics-constrained representation learning, data selection, and uncertainty quantification. Our strategy is transferable to other scattering processes, and other constrained physics problems limited by inconsistent data.
The dynamics of particles in the early universe are described by Boltzmann equations, which involve high-dimensional phase-space integrals. Classical approaches use quadrature integration and evolve the system on a fixed momentum grid, which scales poorly to complicated systems and parameter scans, severely limiting the complexity of processes that can be studied. We introduce Neural Boltzmann Equations (NBEs), which combine three coupled concepts to overcome these limitations. First, particle properties are encoded in physics-inspired neural distribution functions, with parameters that can be predicted using neural networks, enabling efficient parameter scans. Second, phase-space integrals are evaluated with Monte Carlo, using importance sampling tools from collider physics. Third, we use the natural gradient method to evolve the system. After demonstrating the individual benefits of NBEs, we use the framework to perform a precision calculation of the effective number of relativistic neutrino degrees of freedom in the early universe.
Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among existing deep learning?based approaches for solving PDEs, neural operators typically rely on extensive trajectory data, whereas physics-informed meth?ods often exhibit limited stability during long-time extrapolation. For a well-posed autonomous PDE, long-time trajectories can be generated by repeated composition of a fixed-step evolution operator; hence, long-time extrapolation depends on controlling the approximation error of this operator and the propagation of that error under recursive composition. Accordingly, we propose a numerical-prior-guided, physics-constrained method trained without ground-truth trajectory supervision: a low-cost numerical prior reduces the difficulty of approximating the one?step evolution operator, while a weak-form PDE residual provides a computable proxy for the one-step error term in the error?propagation bound. We validate the method on five benchmark cases spanning four PDE classes and compare it with ten physics?informed learning methods under a unified protocol that excludes ground-truth trajectories from training and model selection. The results indicate that, in all five cases, the proposed method reduces long-time extrapolation error relative to the numerical prior and outperforms the best competing baseline in each case, thereby improving long-time simulation accuracy across different PDEs without ground-truth trajectory supervision. The source code developed for this paper will be made publicly available upon acceptance of the manuscript.
Conventional simulation of current-driven magnetization relies on fine-step integration of the spin-transfer-torque Landau--Lifshitz--Gilbert equation, creating a computational bottleneck in parameter sweeps and control searches. In this work, we propose a physics-constrained neural flow map that learns finite-time dynamics directly on the unit sphere. The model maps the current magnetization, spin-torque strength, and requested time span to a future state in a single forward pass. Tangent-space projection and spherical retraction preserve unit magnetization during recursive, composition-consistent rollout. We validate the framework on single-spin trajectories under in-domain torques and previously unseen but stronger drive. Beyond the training horizon, it achieves an in-domain root mean square error of $0.00425$ with norm drift at the $10^{-7}$ level. The flow outperforms an adapted Long Short-Term Memory (LSTM) in in-domain accuracy and geometric stability, although the LSTM retains slightly lower out-of-distribution state error. The resulting geometry-preserving propagator reduces reliance on fine-step integration and enables physically admissible long-horizon prediction.
Accurate modeling of sea ice concentration (SIC) evolution is essential for polar climate assessment and short?range sea ice prediction. Numerical and data-driven approaches constitute major foundations for SIC modeling, but the former often require complex parameterizations and substantial compu?tation, whereas the latter rarely encode physical dependencies explicitly. This study presents the Physics-Informed Hybrid Ice Model (PIHIM), a differentiable data-driven hybrid ice model for daily SIC evolution that organizes its network structure according to the physical dependencies encoded in the sea ice continuity equation and explicitly accounts for dynamical transport, ther?modynamically driven areal growth and loss, and unresolved local processes. PIHIM preserves the representation capacity of deep learning while providing a process-decomposed formulation of ice displacement, freeze-melt areal change, and local error closure. Two evaluation settings are adopted: reanalysis-forced simulation examines SIC evolution stability under reanalysis forcing, and forecast-forced prediction assesses short-range performance un?der forecast-forced conditions, with reanalysis and observational SIC serving as verification references. Results indicate enhanced ice-edge preservation and error-growth control in reanalysis?forced simulation, while PIHIM retains measurable short-range prediction skill under forecast-forced conditions. Our code will be made publicly available after the paper is accepted.
Rafid Umayer Murshed, Saif Ur Rahman, Mingyue Tang +1cs.LG cs.AI
Radio maps are essential for wireless decision-making tasks such as access-point placement, coverage planning, and localization, but their fine spatial details are governed by complex propagation effects and are costly to simulate accurately. Machine learning offers a path to high-fidelity radio-map prediction without running expensive high-fidelity simulations for every scene. However, generating high-quality training labels at scale is also difficult: the affordable labels come from finite-ray simulations, which are richer than low-fidelity inputs but carry residual Monte Carlo noise. We address this challenge with Physics-Unrolled Hybrid Neural Operator (PU-HNO), a three-stage cascade that predicts high-fidelity indoor radio maps from low-fidelity ray-tracing outputs and scene priors by progressively capturing reflection, diffraction, and scattering effects, rather than treating radio maps as generic images. We prove that, under conditionally unbiased label noise, the model can learn stable propagation structure and outperform its own training labels. Experiments across diverse floorplans show that PU-HNO outperforms image-to-image baselines, wireless learning models, and monolithic neural operators across both image-quality and wireless deployment metrics.
High-fidelity finite-element simulations can provide accurate numerical predictions for side-branch resonators, but large simulation datasets are expensive to generate and purely data-driven surrogates may become unreliable when simulation-labelled data are scarce. This study develops an analytical-prior learning framework that reuses a low-cost analytical model to improve data efficiency under limited high-fidelity simulation budgets. Two complementary routes are considered. When the analytical model remains available at inference, it is retained as an explicit baseline and the simulation data are used to learn only the analytical-to-simulation discrepancy. When a self-contained predictor is required, the analytical mapping is first distilled from abundant low-cost evaluations into a learned prior and then calibrated with the limited simulation data. The framework is evaluated on rectangular side-branch Helmholtz resonators using 86 simulation-labelled geometries and 8,998 non-overlapping analytical-only geometries. The analytical model achieved a mean absolute error (MAE) of 1.333 Hz. Direct support vector regression (SVR) achieved 3.375 Hz, while residual SVR reduced the MAE to 0.426 Hz. A direct multilayer perceptron (MLP) achieved 1.109 Hz, whereas analytical-prior pretraining reduced the error to 0.556 Hz with frozen-prior residual adaptation and 0.371 Hz with full-model fine-tuning. Across training budgets of 20 to 70 simulation-labelled cases, both analytical correction and analytical-prior pretraining consistently improved data efficiency relative to direct learning. These results show that analytical prior information can substantially improve high-fidelity prediction when simulation data are scarce, with explicit correction and prior distillation serving complementary deployment needs.
Xinling Yu, Yixing Li, Ziyue Liu +4cs.LG physics.data-an
Thermal-aware optimization of multi-die 3D integrated circuits evaluates many designs, each a costly heat-equation solve. Operator-learning surrogates replace this solve with a fast forward pass, ideally trained from physics alone, without labeled data. DeepOHeat-v1 made such surrogates fast and trustworthy, but only on low-contrast geometries. High-contrast multi-die stacks break it in two ways: discontinuous conductivities make the continuous physics loss ill-defined at material interfaces, and ill-conditioning ($κ_2(A_h) \approx 6 \times 10^4$) puts the discretized strong-form loss beyond first-order optimization. We propose DeepOHeat-v2 to overcome both. First, we train on a discretized physics loss that handles the discontinuities natively; its energy form reduces the prediction-space loss-Hessian conditioning from $κ^2$ to $κ$, and a matrix-preconditioned optimizer cuts the mean peak temperature error from over 30 K to 0.55 K. Second, because optimization leaves the training distribution, we propose a self-improving framework: a hotspot trust gate sends flagged placements to a reference solver, and the surrogate incrementally retrains on the refined solutions, keeping an update only when it improves held-out validation error. On a multi-die benchmark, the surrogate-true peak gap on the returned design falls from 1.12 K to 0.11 K, matching a solve-at-every-step optimizer while running $56\times$ faster.
Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.
Amanda Sheron Gamage, Niloofar Mehrnia, James Grosscs.AI
Ultra-reliable low-latency communication (URLLC) requires precise identification of spatial regions where the signal-to-noise ratio (SNR) falls below an outage threshold. In this context, an outage refers to instances in which SNR falls below a specified threshold, which, for URLLC, can be as stringent as the 0.1% quantile of the SNR distribution. Traditional generative radio map models tend to focus on reconstructing average signal levels, often overlooking the low SNR that is crucial for accurate outage prediction. To address this limitation, we introduce a physics- and tail-informed VAE-EVT (variational autoencoder-extreme value theory) framework that distinctly models both the bulk and tail distribution of SNR. Our approach begins with a physics-informed preprocessing stage that extracts deterministic features, including line-of-sight, shadowing, and distance, from the scene geometry. A dual-latent encoder then captures the bulk SNR using a Gaussian mixture and the tail using a generalized Pareto distribution (GPD). By employing a modified variational objective, the model is trained to jointly supervise both regimes, ensuring focused attention on extreme fading events. Evaluated on the RadioMapSeer dataset, our method achieves an SNR RMSE of 4.83 dB in the outage region defined by the low threshold of 0.1% SNR quantile. This significantly outperforms the state-of-the-art GAN-based model, which records an SNR RMSE of 21.90 dB, with the performance gap widening as the outage threshold becomes more stringent.
Mushtaq Ali, Muzamil Tariq, Niaz Ali Khancs.LG math-ph quant-ph
Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.
Manas Dogra, James Halverson, Joydeep Naskarhep-th cs.LG
We construct spinning conformal fields from neural networks and the embedding formalism, computing their two-, three- and four-point functions in examples, building on scalar conformal field techniques introduced in \cite{Halverson:2024axc}. For a particular ensemble of i.i.d. neurons we recover the 4d Maxwell CFT in the infinite-width limit.
Žan Gorenc, Žiga Gradišar, Felix Mütter +2stat.AP cs.AI
Estimating the distribution of relaxation times (DRT) fromelectrochemical impedance spectroscopy (EIS) is an ill-posed inverse problem that is highly sensitive to regularisation choices. We propose a physics-informed convolutional autoencoder that estimates DRT directly from EIS data without spectrum-specific tuning. A discretised relation between impedance and the DRT is embedded in the training process, constraining the network to produce impedance-consistent distributions. The model resolves overlapping relaxation processes in synthetic two-ZARC spectra and accurately reconstructs measurements from three independent solid oxide fuel and electrolysis cell datasets, with range-normalised errors below 1.1%. Decoder-probe analysis shows that the learned latent representation is organised according to relaxation timescale. Distances in this latent space capture operating changes, hydrogen-shortage events, and long-term degradation. The same lightweight architecture is applied across all datasets without modification, providing consistent DRT estimation and an interpretable basis for condition monitoring.
Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.
Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs. In this work, we propose Structure-Preserving Epistemic Neural Networks (S-PENNs), a general framework for UQ in scientific machine learning models with hard architectural constraints, and instantiate it for GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) dynamics. S-PENNs preserve the structural constraints of a pretrained model by attaching lightweight epinets to its constrained components, ensuring that every sampled realization remains physically admissible by construction. When applied to GENERIC dynamics, such a proposed framework yields thermodynamically consistent rollouts that preserve the first and second laws. Furthermore, we combine S-PENNs with split conformal prediction as a post-hoc calibration method to produce prediction intervals with finite-sample marginal coverage guarantees. We validate S-PENNs on three numerical examples: a harmonic oscillator coupled to a heat bath and an idealized chemical motor, both governed by ODEs, and a one-dimensional viscoplastic model governed by PDEs. Across all three examples, S-PENNs produce thermodynamically consistent stochastic realizations and well-calibrated prediction intervals while reducing the computational cost by about one to three orders of magnitude compared to deep ensembles. Although the present study focuses on GENERIC dynamics, S-PENNs can be extended more broadly to scientific machine learning models in computational mechanics with either hard or soft constraints.
Industrial time-series signals, such as turbine temperature and rotational speed in aero-engines, are essential for monitoring the health and operational status of complex dynamical systems. However, collecting such data is often limited by harsh environments (e.g., high temperature and high pressure) and the high cost of experimental testing. To address this challenge, we introduce PhysDGM, a stepwise physics-embedded diffusion generative model for synthesizing time-series data that are consistent with the underlying physical laws of dynamical systems. PhysDGM embeds physical laws directly into each reverse diffusion step of the generative process, ensuring trajectory-level physical consistency, rather than enforcing constraints only at the final output. A large-scale AI-synthetic dataset (4.4 million samples, 20x scale-up) constructed by PhysDGM demonstrates strong fidelity across 34 datasets spanning turbofan engines, aero-engines, batteries, and chemical processes. After incorporating the synthetic data, the downstream task performance substantially surpassed that using real data alone by 48% for remaining useful life prediction, 15% for health indicator estimation, 22% for state-of-health assessment, and 20% for fault diagnosis. Moreover, it requires 10-20x less training data than existing approaches, substantially reducing the high cost of data collection in dynamical systems. We further demonstrate PhysDGM's potential in identifying early-stage faults in aero-engines by incorporating AI-synthesized data. In summary, PhysDGM provides a solid foundation for generating physically consistent industrial time-series, paving the way for expanding physics-guided AI into diverse data-scarce environments, including both industrial machinery and complex chemical reaction dynamics.
Thermo-mechanical compliant devices are commonly designed with small-strain linear elasticity and temperature-independent material properties, even though they might operate hundreds of kelvin above ambient where both assumptions are questionable. In this work, we quantify the effect and cost of each assumption in multi-material topology optimization of thermally actuated compliant devices. To this end, we introduce a physics-informed, simultaneous analysis-and-design framework with (i) a finite-strain quadratic-Hencky (logarithmic-strain) constitutive model whose isotropic thermal eigenstrain admits an exact additive split in log-strain space, and (ii) temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium--copper--steel material system. We optimize a thermal actuator and a thermal gripper at three design temperatures under both a baseline model and the full physics, subject to mass and manufacturability constraints. Every converged design is re-evaluated by verified nonlinear finite element solvers in the full factorial of constitutive law and property model. The comparison between the two factors reveals that the constitutive law is the decisive modeling choice: These devices work as linkages where linear kinematics mistakes rotation for compressive strain; its error therefore grows with the design temperature and concentrates on the very layouts that exploit rotation best. Because a linear optimizer also steers away from the rotation-rich mechanisms that would expose this bias, the model can deceptively appear trustworthy when validated against its own designs. Designing with the full physics yields consistently stronger and more temperature-robust devices at a modest increase in design-time cost.
Physically consistent motion planning remains a fundamental challenge in embodied AI, as generated trajectories must strictly conform to real-world execution dynamics. While latent world models offer a promising approach by predicting these dynamics, existing methods learn unconstrained future representations where absorbed physics remains implicit. Therefore, they fail to form reusable physical knowledge, which compromises reliability in unpredictable open-world navigation. To address this, we propose a novel Energy-Structured Latent World Model (ELWM). Our key idea is to structure the ELWM latent state to explicitly carry energy and momentum, ensuring strictly causal transitions via dissipation and control ports. Trained on multimodal RGB-D and inertial interaction histories, our model guarantees physically consistent predictions. We further implement this for motion planning by constructing Physics-Conditioned Neural Time Fields (PC-NTF), a key technical cornerstone that integrates ELWM into an arrival time field via the Eikonal equation to yield a physically-informed navigation policy. Across held-out scenes, our evaluation reveals significant improvements. Compared to generic latent models, PC-NTF reduces 0.8-s motion-prediction NRMSE from 0.36 to 0.29. Against Active Neural Time Fields, it improves navigation success from 81.3% to 89.7% and SPL from 0.64 to 0.73, while cutting the physical collision rate from 12.1% to 5.8% and the Eikonal residual from 0.083 to 0.031. Beyond these targeted gains, our results demonstrate that embedding explicit physical structures into latent spaces intrinsically bridges the gap between predictive world models and safe, dynamically feasible motion planning.
Christopher Braun, Julian Raible, Marco F. Hubercs.LG cs.AI
In modern industry, keeping complex systems reliable, safe, and efficient hinges on Prognostics and Health Management (PHM). Machine Learning (ML) has largely driven advancements in diagnostics and prognostics, yet purely data-driven models face inherent limitations, such as poor generalization, an inability to infer causal relationships, and a lack of interpretability. Physics-Informed Machine Learning (PIML) helps mitigate these limitations by incorporating prior physical knowledge directly into the ML pipeline, thereby fostering growing interest in its application to PHM. This work investigates how PIML is being leveraged in the context of PHM through a systematic literature review of 212 studies. The review introduces a four-class classification scheme, consisting of observational bias, inductive bias, learning bias, and hybrid approaches, and further categorizes studies by PHM task. Across all four classes, the reviewed studies consistently demonstrate improved predictive performance over conventional baselines across a broad range of assets, although the literature is heavily skewed toward lithium-ion batteries and bearings, and dominated by problem-specific solutions. Overall, the review indicates that physics-informed approaches already provide tangible benefits, whereas claims of improvements concerning some of the aforementioned limitations lack sufficient supporting evidence. Future research should prioritize transferable design patterns, benchmarks comparing integration strategies, and uncertainty-aware models that are lightweight and robust enough for online deployment in real-world settings.
Mattia Scarpa, Evgeny Kusmenko, Francesco Toso +3eess.SY cs.LG
Data-driven health-state estimators for SiC (Silica-Carbide) power modules typically report their performance on a single accelerated-aging campaign, and how that performance transfers to a different failure mechanism is rarely tested. We benchmark five reference methods from the prognostics and condition-monitoring literature against a physics-informed NODE (Neural Ordinary Differential Equation) on two SiC power-cycling campaigns driven by structurally different failure mechanisms, solder-layer fatigue and wire-bond lift-off, under a per-module $k$-fold protocol. The NODE is evaluated under two input regimes that share the rest of the pipeline: the baseline electrical precursors and a set of cumulative thermoelectric features. Every reference method degrades on the wire-bond campaign, with average errors growing and precision decreasing with respect to their performance on the soldered campaign. The NODE fed with the cumulative features keeps its soldered-campaign metrics on both mechanisms, with differences inside the fold-to-fold variance, while the same architecture fed with the baseline precursors falls back to the reference-method cluster. The input representation contributes at least as much as the architecture to failure-mechanism transferability of a health-state estimator.
Mattia Scarpa, Evgeny Kusmenko, Francesco Toso +3eess.SY cs.LG
Silicon carbide (SiC) power modules are increasingly deployed in automotive traction inverters, where condition monitoring is essential to prevent in-service failures. Despite extensive qualification under AQG 324, no consolidated approach exists for in-field health state estimation: physics-of-failure lifetime models lack real-time applicability, purely data-driven architectures require large labeled datasets and generalize poorly, and physics-informed frameworks remain too demanding for embedded deployment. We address SiC MOSFET modules assembled with sintered packaging, which suppresses solder degradation and produces aging behavior distinct from previously studied devices. Instead of the smooth quasi-exponential drift of solder-based modules, the forward voltage drop $V_{DS}$ exhibits multi-regime profiles, with wirebond liftoff events introducing abrupt, non-monotonic perturbations. We propose a condition monitoring framework combining three elements. First, physics-informed features replace raw sensor signals with cumulative damage indicators derived from junction temperature swing, mean junction temperature and a Miner rule accumulator, encoding degradation history in an interpretable form. Second, a monotonicity constraint enforced by gradient penalty regularization embeds the expected degradation direction as a physics-guided prior. Third, a heavy-tailed output distribution replaces the point estimate, giving calibrated uncertainty robust to the out-of-distribution variance introduced by liftoff. On an industrial power cycling dataset from Infineon Technologies, several neural architectures are compared under a strict cross-validation protocol. The full configuration reduces mean absolute error by approximately 70% over purely data-driven baselines and stays stable across all folds, while remaining lightweight enough for embedded deployment.