Mengtao Yan

Bocheng Zeng, Rui Zhang, Runze Mao et al.

Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose \textsc{NPSolver}, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of relying on fully converged numerical solutions or raw PDE residuals, \textsc{NPSolver} utilizes a small number of preconditioned conjugate gradient (PCG) steps to refine its own predictions, providing a more stable and well-scaled training signal. Theoretical analysis confirms that this iterative supervision serves as a well-conditioned error proxy and that a stop-gradient design is essential for optimization stability. To better capture boundary-driven features under mixed boundary conditions, we further introduce the Boundary-Aware Transolver (\textsc{BA-Transolver}) architecture that explicitly separates interior and boundary tokenization. Extensive evaluations on 2D and 3D irregular geometries demonstrate that \textsc{NPSolver} outperforms both physics-informed and data-driven baselines. Furthermore, a downstream thermal control task highlights the model's capability for conducting efficient and reliable gradient-based boundary control. We will release our codes and data at https://github.com/intell-sci-comput/NPSolver.

Runze Mao, Rui Zhang, Xuan Bai et al.

Predicting multiphysics dynamics is computationally expensive and challenging due to the severe coupling of multi-scale, heterogeneous physical processes. While neural surrogates promise a paradigm shift, the field currently suffers from an "illusion of mastery", as repeatedly emphasized in top-tier commentaries: existing evaluations overly rely on simplified, low-dimensional proxies, which fail to expose the models' inherent fragility in realistic regimes. To bridge this critical gap, we present REALM (REalistic AI Learning for Multiphysics), a rigorous benchmarking framework designed to test neural surrogates on challenging, application-driven reactive flows. REALM features 11 high-fidelity datasets spanning from canonical multiphysics problems to complex propulsion and fire safety scenarios, alongside a standardized end-to-end training and evaluation protocol that incorporates multiphysics-aware preprocessing and a robust rollout strategy. Using this framework, we systematically benchmark over a dozen representative surrogate model families, including spectral operators, convolutional models, Transformers, pointwise operators, and graph/mesh networks, and identify three robust trends: (i) a scaling barrier governed jointly by dimensionality, stiffness, and mesh irregularity, leading to rapidly growing rollout errors; (ii) performance primarily controlled by architectural inductive biases rather than parameter count; and (iii) a persistent gap between nominal accuracy metrics and physically trustworthy behavior, where models with high correlations still miss key transient structures and integral quantities. Taken together, REALM exposes the limits of current neural surrogates on realistic multiphysics flows and offers a rigorous testbed to drive the development of next-generation physics-aware architectures.

Mengtao Yan, Qi Wang, Haining Wang et al.

Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence conditions, leading to substantial computational costs. Although machine learning has demonstrated better efficiency, they typically suffer from issues of interpretability, generalizability, and data dependency. Hence, we propose a learnable and differentiable finite volume solver, called LDSolver, designed for efficient and accurate simulation of fluid flows on spatiotemporal coarse grids. LDSolver comprises two key components: (1) a differentiable finite volume solver, and (2) an learnable module providing equivalent approximation for fluxes (derivatives and interpolations), and temporal error correction on coarse grids. Even with limited training data (e.g., only a few trajectories), our model could accelerate the simulation while maintaining a high accuracy with superior generalizability. Experiments on different flow systems (e.g., Burgers, decaying, forced and shear flows) show that LDSolver achieves state-of-the-art performance, surpassing baseline models with notable margins.