A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration

The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error. Forcing all sources into one black box makes mechanism attribution and constraint preservation unauditable; forcing every mechanism into one equation family discards mature domain solvers. We propose SD-GWM, a Structural Dynamics Graph World Model as an executable structural contract: nodes declare self-dynamics S, edges declare neighbor graph-coupled dynamics N---both fixed-form mechanism assets (rules, ODEs, solvers) calibrating only authorized parameters. An optional bounded residual R concentrates learnability, while a global projection maps states to feasibility, enforcing constraints without guaranteeing accuracy gains. On eight pre-registered research questions, SD-GWM delivers (i) heterogeneous integration: rules and solvers plug in natively; (ii) semantic fidelity: disabling R preserves source semantics bit-for-bit, with four theory properties under explicit proof/empirical boundaries; (iii) auditable governance: stepwise traces enable counterfactual fault localization (top-1 = 1.0) without post-hoc approximations. On a semi-synthetic flood testbed and USGS streamflow, SD-GWM reduces constraint violations to floating-point tolerance in analytical tests and to zero in semi-synthetic and real-data cases. Persistence matches SD-GWM in calm periods, but during a 254-day extreme-flood shift persistence and all neural baselines collapse (90-min RMSE 892-3007 cfs) while SD-GWM holds at 108 cfs (8-28x gain). The bounded residual cuts RMSE ~50% only under backbone bias. We position SD-GWM not as a universally superior forecaster, but as a verifiable substrate for auditable, constraint-safe spatiotemporal mining.

Directional Constraints for Efficient Exploration in Safe Reinforcement Learning

Reinforcement Learning has revolutionized the landscape of robotic research, allowing robust learning of complex robotic skills in simulation. However, real-world deployment in open-ended environments requires strong safety guarantees to prevent dangerous or harmful behaviors. Safe Reinforcement Learning methods address this requirement by enforcing safety constraints. Nevertheless, learning under constraints often reduces learning speed and could lead to suboptimal task performance, as the agent must solve a more complex constrained optimization problem compared to unconstrained settings. To tackle this issue, in this work, we propose an extension of the ATACOM framework, a state-of-the-art reliable safety layer that can be integrated with existing Reinforcement Learning algorithms to enforce constraints derived from prior knowledge of the system or learned directly from data. Our proposed method, named ATACOM Directional Constraints (ATACOM-DC), significantly improves the safety-performance trade-off by introducing directional constraints that distinguish between actions approaching and moving away from constraint boundaries, activating constraint enforcement only when necessary. We evaluate our method across a range of challenging robotic control tasks in simulation, analyzing both constraint-violation costs and achieved task performance. Code and additional material at https://atacom-dc.robot-learning.net.

PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection

While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.