physics-based simulation

This work proposes implicit Finite Operator Learning (iFOL), a physics-informed operator learning framework for multiphysics problems governed by coupled partial differential equations on arbitrary domains, which operates without requiring ground-truth labeled data. Built upon the finite element weighted residual formulation, iFOL establishes a resolution-independent mapping from input parameters to the solution space and provides a unified treatment of complex geometries and multiphysics coupling. Implemented within the Folax system on the JAX platform, the approach integrates FNO, DeepONet, and iFOL, leveraging finite element residuals to construct physics-constrained loss functions. Experiments demonstrate that iFOL achieves high efficiency on complex geometries in two- and three-dimensional nonlinear thermo-mechanical coupling and industrial casting scenarios, while FNO excels in accuracy on regular domains; furthermore, a single-network end-to-end training strategy significantly outperforms baseline methods.

FDTD-based electromagnetic simulations suffer from poor portability, high development overhead, and performance bottlenecks on modern hardware. To address these challenges, this paper introduces the first MLIR/LLVM-based domain-specific compiler for FDTD. It models the 3D FDTD kernel as semantically explicit 3D tensor operations and proposes a novel high-order tensor abstraction with an automated optimization framework supporting loop tiling, fusion, and vectorization. The compiler features hardware-aware, end-to-end code generation across heterogeneous platforms (x86 and ARM). Experimental evaluation demonstrates up to 10× speedup over NumPy baselines across multiple architectures. By eliminating manual tuning, it overcomes performance fragmentation and non-portability inherent in conventional approaches, thereby significantly improving simulation efficiency, scalability, and deployment flexibility.

This study addresses the high computational cost and steep learning curve associated with electromagnetic simulation modeling. We propose a conversational, LLM-driven automation framework for electromagnetic simulation, centered on Google Gemini 2.0 Flash as the reasoning engine and tightly integrated with Gmsh (geometry generation), GetDP (finite-element solver), and Python (workflow orchestration). The method enables users to specify physical configurations, boundary conditions, and solution objectives via natural language, automatically generating executable simulation scripts, solving 2D eddy-current problems, and delivering customized post-processing and concise result summaries. Key contributions include the first end-to-end, natural-language-to-simulation pipeline for electromagnetic analysis and seamless integration of domain-specific solvers with modern LLMs. Experimental evaluation across diverse conductor geometries demonstrates high modeling accuracy, strong generalization capability, and substantial reductions in user expertise requirements—thereby improving modeling efficiency and human–machine interaction.

Sensitivity analysis for steady-state heat conduction in heterogeneous materials—characterized by strong phase contrast and temperature-dependent properties—is computationally expensive when performed via conventional adjoint methods. Method: This paper proposes the Finite Operator Learning (FOL) framework, which tightly integrates neural operators with finite element discretization. FOL embeds physical constraints—including the weak-form energy functional, boundary conditions, and residual stationarity—into a multi-objective loss function, and combines Sobolev-norm training with feedforward networks to jointly predict both PDE solutions and their sensitivities to design parameters in an end-to-end manner. Contribution/Results: FOL requires neither labeled training data nor adjoint computations, ensuring strong physics consistency. It directly outputs high-fidelity solutions and accurate gradients, enabling tangent-matrix-driven microstructural thermal optimization. By eliminating iterative adjoint solves, FOL significantly reduces sensitivity analysis cost while preserving numerical robustness and physical fidelity.

Neural operator training is severely constrained by reliance on data generated via traditional numerical solvers, which are computationally expensive, discretization-dependent, and introduce approximation errors. Method: We propose a solver-free backward synthetic data generation framework: candidate solutions $u_j$ are randomly sampled from the solution space (e.g., $H_0^1(Omega)$), and their exact source terms $f_j = mathcal{L}u_j$ are computed directly via automatic differentiation—yielding infinite, zero-error $(f_j, u_j)$ training pairs without numerical discretization. Contribution/Results: This work introduces the first “solution-to-source” inverse generation paradigm, eliminating dependence on numerical solvers while preserving mathematical rigor and computational scalability. Experiments demonstrate that neural operators trained exclusively on synthetic data achieve generalization performance on multiple PDE benchmarks comparable to—or even exceeding—that of models trained on solver-generated data.

This work addresses the challenges of high-fidelity simulation in fusion energy systems—specifically, geometric modeling, multiphysics coupling, and the integration of particle and continuum methods—by proposing a unified framework that seamlessly combines commercial CAE software with existing fusion codes. The framework enables accurate representation of complex geometries, automatic generation of unstructured meshes, and efficient coupling between particle transport and continuum solvers. The resulting simulation workflow significantly enhances geometric fidelity for critical components and strengthens capabilities in multiscale, multiphysics co-simulation, while maintaining strong scalability and computational efficiency.

This work addresses the frequent mismatch between user-specified physical intent and the actual behavior of multiphysics simulation code generated by large language models, often due to erroneous implementations of partial differential equations (PDEs). To bridge this gap, we propose a PDE-structure-based intent verification method that deterministically reconstructs the governing equations implicitly encoded in the generated code and compares them against the user’s intended PDEs, enabling semantic correctness validation and iterative refinement. We introduce, for the first time, a formal metric termed the Intent Fidelity Score (IFS) to quantify alignment with physical intent, establish a PDE-driven feedback loop, and demonstrate compatibility with major PDE frameworks including MOOSE, FEniCS, and FreeFEM. Evaluated on 220 cases in MooseBench, our approach substantially improves IFS—by 0.22–0.41 on challenging instances with initial IFS < 0.7—while audits reveal that execution-only repair strategies still yield physically incorrect results in 39–40% of cases.

This work addresses the limited reusability of traditional data-driven thermal simulation methods for 3D integrated circuits (3D-ICs), which rely heavily on large volumes of high-fidelity finite element data. To overcome this challenge, the authors propose Therm-FM, the first approach to transfer a pre-trained partial differential equation (PDE) foundation model to 3D-IC thermal simulation. By integrating neural operators with multi-fidelity learning and introducing a thermal equivalent modeling mechanism, Therm-FM enables highly accurate and efficient prediction of both steady-state and transient thermal fields using only minimal target-domain data. Evaluated on public and industrial-scale benchmarks, Therm-FM surpasses state-of-the-art methods with less than 20% of the training data, reducing average errors by up to 10.6×. Moreover, cross-chip adaptation requires merely 10–30 samples to match or exceed the performance of full-data baselines.

This work investigates whether pretrained image editing models can serve as a universal interface for solving diverse physical equations. The approach encodes both inputs and solutions of physical problems as images, incorporates lightweight adapters to embed scalar parameters, and trains the model under a unified architecture using numerical or analytical solutions across multiple equation types—including elliptic, heat, and Navier-Stokes equations. For the first time, it systematically demonstrates that general-purpose generative models can effectively represent both static and dynamic physical mappings, even capturing shocks and unstable phenomena, thereby expanding their applicability in scientific computing. Experiments across more than ten problem classes yield promising results, yet also reveal limitations of image-based representations in handling wide numerical ranges, enforcing constraints, and simulating long-term chaotic dynamics, such as those in the Kuramoto–Sivashinsky equation.

This work proposes a novel approach to black-box testing of Functional Mock-up Units (FMUs) by integrating large language models (LLMs) with a human-in-the-loop mechanism. Addressing the inefficiency and poor interpretability of traditional FMU-based dynamic simulation testing—which relies on manually crafted scenarios—the method automatically generates structured Given-When-Then test objectives from FMU interface and functional specifications, and constructs complete test plans comprising input sequences and assertion oracles. Upon simulation execution, the framework produces visualizable logs and statistical evaluation metrics. The approach significantly enhances test design efficiency and result interpretability, facilitates test asset reuse, and demonstrates effectiveness on a lubricating oil cooling system by autonomously generating executable test scenarios and delivering objective-level pass-rate analysis.