neural-physics simulation

This work addresses the silent failure of neural surrogates in simulating physical systems with discontinuities such as shocks and fronts. The authors propose a hybrid neural world model that employs a single network to directly predict arbitrary future states in continuous time, implicitly encoding discontinuity locations without requiring explicit supervision of jump points. By leveraging forward propagation to generate trajectory-level error maps, the method precisely localizes anomalous regions and integrates a fallback mechanism based on a reference solver alongside unsupervised uncertainty estimation, enabling efficient inference and adaptive correction. Evaluated on reaction–diffusion, compressible Euler, and rigid-body collision systems, the model achieves 26–72× CPU speedup; incorporating error-map-based fallback reduces approximation error by approximately 50%, substantially outperforming existing unsupervised baselines.

Balancing computational efficiency and accuracy remains challenging in solving multiscale, dynamic, multiphysics partial differential equations (PDEs). Method: This paper proposes an adaptive hybrid solver integrating the finite element method (FEM) with a physics-informed DeepONet. It introduces, for the first time, a dynamic subdomain decomposition mechanism based on the Schwarz alternating method, enabling automatic subdomain evolution to capture transient fine-scale features; within each Newmark time step, DeepONet is embedded to establish a tightly coupled FEM–neural operator architecture—eliminating the need for remeshing. Contribution/Results: The solver achieves 20% speedup on static and dynamic solid mechanics problems while maintaining global error below 1%. It rigorously enforces inter-subdomain solution continuity, removes dependence on fine meshes, and significantly suppresses long-term error accumulation. This work establishes a new paradigm for multiscale physical modeling—delivering both high fidelity and high efficiency.

This work addresses the lack of a unified understanding of the design principles, applicability, and performance differences between Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), which hinders the development of reliable data-driven PDE solvers. It proposes the first unified analytical framework that systematically characterizes the design space of both approaches along three dimensions: learning objectives, mechanisms for embedding physical structure, and strategies for computational load distribution. By elucidating the intrinsic connections and fundamental distinctions between these methods, the study not only clarifies the positioning and performance origins of existing techniques but also provides theoretical guidance and novel pathways for designing efficient and robust PDE solvers that effectively integrate physical priors with data-driven learning.

Pure data-driven fluid surrogate models suffer from catastrophic failure due to error accumulation, while existing AI-CFD hybrid approaches lack automation, robustness, and scalability. This paper proposes XRePIT: a physics-aware hybrid simulation framework based on closed-loop feedback, integrating residual-guided learning, physics-informed neural networks (PINNs), and conventional CFD solvers for end-to-end supervised training. XRePIT achieves unprecedented stable acceleration over 10,000 time steps, with built-in automatic error correction, strong generalization—including to unseen boundary conditions—and native 3D scalability. Validated on multi-scale real-world 2D/3D flow fields, XRePIT delivers up to 4.98× speedup versus full CFD, thermal field relative error ≈10⁻³, and low-amplitude velocity dynamics error <0.01 m/s. These results substantially overcome key practical limitations of prior hybrid methods in accuracy, stability, and deployability.

Hybrid neural fields (e.g., Instant NGP) suffer from inaccurate spatial derivative estimation, introducing severe artifacts in neural rendering, physics simulation, and PDE solving. To address this, we propose the first high-fidelity derivative correction framework tailored for hybrid neural fields. Our method employs plug-and-play post-processing via local polynomial fitting to enhance derivatives, coupled with a lightweight, self-supervised gradient consistency loss for fine-tuning the hash grid + MLP architecture. Crucially, it operates without retraining pre-trained models, preserving original signal fidelity while substantially improving derivative accuracy. Experiments demonstrate that our approach eliminates high-frequency rendering artifacts, enhances stability in contact force computation for rigid-body collision simulation, and significantly reduces gradient errors in PDE solving. By delivering geometrically and physically consistent derivatives, our framework enables robust downstream applications in graphics, simulation, and scientific computing.

This work addresses the challenge that existing frameworks struggle to efficiently support the direct development of multiphysics coupling solvers and parallel adaptive simulations. We propose a portable, reproducible cross-language framework that, for the first time, tightly integrates Trixi.jl with deal.II to construct a strongly coupled partitioned solver for Newtonian self-gravitating hydrodynamics. By combining a strong coupling strategy, cross-language interoperability, adaptive mesh refinement, and parallel computing, our framework substantially simplifies the development of coupled solvers. Numerical experiments demonstrate high-order convergence, physical consistency, and effective adaptivity of the algorithm, while also exhibiting favorable strong scaling performance in parallel execution.

This work addresses the challenge of spurious fixed points in hybrid deep learning–based PDE solvers, which often arise from a mismatch between training objectives and iterative strategies, leading to large physical residuals and unreliable convergence. To overcome this limitation, the authors propose Physics-Aware Anderson Acceleration (PA-AA), which integrates neural operators—such as DeepONet and Fourier Neural Operators—with classical numerical methods. Unlike conventional acceleration techniques that focus on update increments, PA-AA explicitly targets the reduction of physical residuals, thereby aligning the optimization trajectory with physical consistency. Experimental results demonstrate that PA-AA significantly enhances convergence reliability, avoids residual stagnation within fewer iterations, and effectively mitigates the failure modes commonly observed in traditional hybrid solvers.

Traditional neural surrogate models struggle to correct violations of partial differential equation (PDE) constraints and exhibit limited out-of-distribution generalization. Existing hybrid approaches based on residual minimization are computationally expensive and unstable, particularly in ill-posed systems where small residuals do not guarantee accurate solutions. This work proposes the Error-conditioned Neural Solver (ENS), which abandons the paradigm of using residuals as optimization objectives and instead explicitly encodes them as network inputs for the first time. This enables the model to perceive the structure of the error space and learn iterative correction strategies. ENS employs an end-to-end trainable architecture that requires no external optimizer and achieves state-of-the-art accuracy across four PDE families—reducing errors by an order of magnitude on turbulent Kolmogorov flow—while supporting zero-shot parameter variations and cross-equation transfer, significantly enhancing robustness and accuracy under ill-posed conditions and distribution shifts.