Neural network surrogates are an emerging alternative to traditional electromagnetic wave simulators like finite-difference time-domain (FDTD); their goal is to replace rigorous physical simulations with pre-trained neural networks that solve wave-scattering forward and inverse problems orders of magnitude faster. However, nonrecurrent, single-step surrogates have scaled only to a few tens of simulation variables. Here, we show that this barrier can be overcome by dynamically generating salient training examples during training, rather than randomly sampling the large space of possible examples. We introduce an algorithm that runs in parallel with surrogate training, using gradient ascent to search refractive-index and source configurations for cases where the surrogate disagrees with a full-wave ground-truth simulator. We also use source and ground-truth normalization with an evolving replay dataset to stabilize and accelerate learning. Using this approach, we train a fast, single-step surrogate for two-dimensional wave scattering with up to 41,772 controllable variables, including dense, freely configurable grids of refractive indices and complex-valued sources. The resulting neural surrogate is robustly accurate across diverse structured and unstructured examples and generalizes inductively to larger domains, reaching over 3 million controllable variables without retraining, a $73.8\times$ increase. We demonstrate the surrogate on large-scale forward simulations and inverse design of freeform beam splitters and gradient-index (GRIN) lenses up to 98 wavelengths wide, showing comparable or better performance than FDTD-based designs, with speedups from $1.29\times$ to $26.5\times$. These results demonstrate a practical path toward fast, robustly accurate, inductively scalable neural simulators for photonic inverse design and other wave-scattering inverse problems.
Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.
Developing foundational neural simulators for Partial Differential Equations (PDEs) requires robust generalization across diverse physical parameters and boundary conditions. However, current deep learning approaches largely face a structural trade-off between condition-agnostic deployment and physical fidelity. Purely data-driven operators infer the underlying physics implicitly and thus lack the explicit constraints needed to ensure physically valid solutions across varying domains, rendering the learning problem ill-posed. On the other hand, Physics-Informed Neural Networks (PINNs) enforce rigorous physical constraints but necessitate costly, instance-specific optimization. Furthermore, the massive scale of emerging foundational operators has severely degraded their inference speeds, making them computationally uncompetitive with traditional numerical solvers. To address this bottleneck between condition-agnostic deployment, physical rigor, and inference efficiency, we propose a \textit{Generalized Neural Operator}. By formalizing the classical conditions for well-posedness within neural operators, our framework demonstrates the theoretical benefits of explicitly conditioning on PDE parameters and boundary conditions. To implement this synthesis without compromising computational speed, we introduce three novel architectural components: a parameter-gated mixture of kernels for efficient parameter generalization, a generalized boundary transfer operator that projects arbitrary boundary constraints into a unified latent Dirichlet representation, and a specialized training objective to ensure stability. Extensive experiments demonstrate that our theoretically grounded approach achieves superior generalization across heterogeneous physical regimes while maintaining strict inference efficiency comparable to conventional numerical baselines.
Embodied navigation aims to build agents that interpret multimodal goals, reason in 3D space, and reach target destinations reliably in the real world. However, progress remains constrained by the lack of scalable, high-fidelity, and physically grounded interactive environments. Although real-world scanned datasets offer visual realism, they are limited by scale. In contrast, synthetic simulators scale more easily but often exhibit large sim-to-real gaps. We introduce Image2Sim, a real-time neural simulation framework that constructs high-quality interactive environments from posed RGB-D image sequences. The central idea is to decouple 3D spatial anchoring from photorealistic observation synthesis. For scene construction, Image2Sim uses a feed-forward feature Gaussian model that lifts posed RGB-D observations into a 3D feature-Gaussian representation in a single pass. For rendering, we propose a Geometry-Aware One-Step Pixel Flow model that transforms sparse and noisy Gaussian projections into high-quality panoramic RGB-D observations. Image2Sim also serves as a fully automated embodied data engine that generates high-fidelity observations, executable actions, and diverse navigation instructions at scale. It converts large collections of videos and images into nearly 20K interactive scenes and synthesizes more than 10 million navigation training samples. Navigation models trained entirely in these neural environments achieve strong improvements on major benchmarks and transfer effectively to real-world zero-shot settings. These results suggest that scalable neural simulation can serve as a practical training substrate for embodied navigation at scale.