AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies

Numerical solvers for partial differential equations (PDEs) are core computational tools in science and engineering. Building reliable PDE solvers requires not only executable code, but a numerical solver strategy, a set of decisions about discretization, stabilization, solver configuration, and resolution control, that matches the PDE structure. Recent LLM-based coding agents have begun to reduce the programming burden by generating and debugging solver implementations. However, they typically move directly from a PDE problem to solver code, leaving the solver strategy implicit in implementation details. Feedback from a failed solve is therefore routed back to code edits rather than to the underlying strategy, so numerical decisions remain hard to check before code is generated and hard to revise using numerical evidence when it fails. To address this limitation, we propose AutoPDE, a code agent that maintains the solver strategy as an explicitly represented object throughout the solving process: an independent, inspectable object that is built before any code is written and can be revised, using numerical evidence, whenever a solve fails. AutoPDE builds and maintains this object in three stages, all drawing from a library of reusable PDE-solving skills: PDE analysis identifies the equation type and algebraic structure; numerical method selection chooses a numerical method that matches the analysis result and commits to a discretization, stabilization, and linear solver accordingly; and adaptive tuning runs low-cost pilot solves to calibrate resolution and tolerances under the prescribed accuracy and runtime budget. We evaluate AutoPDE on the PDE Agent Bench, where experimental results show that AutoPDE achieves a pass rate of $54.5%$, improving over the strongest baseline by $14.2$ percentage points.

Evolve as a Team: Collaborative Self-Evolution for LLM-based Multi-Agent Systems

LLM-based multi-agent systems (MAS) have emerged as an effective paradigm for complex and long-horizon tasks. However, in real-world tasks, MAS often exhibit various failures during execution and such failures are difficult to eliminate during design. This motivates experience-driven MAS evolution, where a system improves based on its own execution experience. Yet such evolution is challenging because MAS experience is prolonged and intricate, interleaving multiple agents' execution chains and communication messages, which makes it difficult to identify what should be improved. To address this challenge, we propose Meta-Team, an experience-driven MAS evolution framework based on collaborative self-evolution. Meta-Team preserves the execution context of each agent and coordinates post-task communication, enabling agents to exchange distributed evidence for evolution. Building on this design, Meta-Team conducts multi-scale self-evolution, transforming execution experience into reusable improvements to agent behaviors, inter-agent coordination, and team-level organization. Across six long-horizon agent benchmarks, Meta-Team consistently outperforms single-agent systems, hand-crafted MAS, and prior MAS evolution methods; further analyses demonstrate that Meta-Team enables more reliable and scalable MAS self-evolution.

PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation

PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only understanding the mathematical structure of PDEs, but also selecting appropriate discretization schemes and solver configurations, and correctly implementing the resulting formulations in finite-element method (FEM) libraries. Existing code generation benchmarks mainly evaluate syntactic correctness, or success on predefined test cases. To our knowledge, there is currently no publicly available benchmark specifically for PDE-to-solver code generation, and general-purpose code benchmarks do not fully capture the unique challenges of numerical PDE solution, such as ensuring solver accuracy, efficiency, and compatibility with professional FEM libraries. We introduce PDEAgent-Bench, to the best of our knowledge, the first multi-metric, multi-library benchmark for PDE-to-solver code generation. PDEAgent-Bench contains 645 instances across 6 mathematical categories and 11 PDE families, with common FEM libraries for DOLFINx, Firedrake, and deal.II. Each instance provides an agent-facing problem specification, a reference solution on a prescribed evaluation grid, and case-specific accuracy and runtime targets. PDEAgent-Bench adopts a staged evaluation framework in which generated solvers must sequentially pass executability, numerical accuracy, and computational efficiency checks. Experiments with representative LLMs and code agents show that models can often produce runnable code, but their pass rate drops substantially once accuracy and efficiency requirements are enforced. These results indicate that current agents remain limited in producing numerically reliable and efficient PDE solvers, and that PDEAgent-Bench provides a reproducible testbed grounded in the practical requirements of numerical PDE solving.

DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they often struggle with long-term stability and precision. We identify two fundamental failure modes in existing architectures: (1) local detail blurring, where fine-scale structures such as vortex cores and sharp gradients are progressively smoothed, and (2) global trend deviation, where the overall motion trajectory drifts from the ground truth during extended rollouts. We argue that these failures arise because existing neural operators treat local and global information processing uniformly, despite their inherently different evolution characteristics in physical systems. To bridge this gap, we propose the Dual-Scale Neural Operator (DSO), which explicitly decouples information processing into two complementary modules: depthwise separable convolutions for fine-grained local feature extraction and an MLP-Mixer for long-range global aggregation. Through numerical experiments on vortex dynamics, we demonstrate that nearby perturbations primarily affect local vortex structure while distant perturbations influence global motion trends, providing empirical validation for our design choice. Extensive experiments on turbulent flow benchmarks show that DSO achieves state-of-the-art accuracy while maintaining robust long-term stability, reducing prediction error by over 88% compared to existing neural operators.

N4MC: Neural 4D Mesh Compression

We present N4MC, the first 4D neural compression framework to efficiently compress time-varying mesh sequences by exploiting their temporal redundancy. Unlike prior neural mesh compression methods that treat each mesh frame independently, N4MC takes inspiration from inter-frame compression in 2D video codecs, and learns motion compensation in long mesh sequences. Specifically, N4MC converts consecutive irregular mesh frames into regular 4D tensors to provide a uniform and compact representation. These tensors are then condensed using an auto-decoder, which captures both spatial and temporal correlations for redundancy removal. To enhance temporal coherence, we introduce a transformer-based interpolation model that predicts intermediate mesh frames conditioned on latent embeddings derived from tracked volume centers, eliminating motion ambiguities. Extensive evaluations show that N4MC outperforms state-of-the-art in rate-distortion performance, while enabling real-time decoding of 4D mesh sequences. The implementation of our method is available at: https://github.com/frozzzen3/N4MC.

Advanced long-term earth system forecasting by learning the small-scale nature

Reliable long-term forecast of Earth system dynamics is heavily hampered by instabilities in current AI models during extended autoregressive simulations. These failures often originate from inherent spectral bias, leading to inadequate representation of critical high-frequency, small-scale processes and subsequent uncontrolled error amplification. We present Triton, an AI framework designed to address this fundamental challenge. Inspired by increasing grids to explicitly resolve small scales in numerical models, Triton employs a hierarchical architecture processing information across multiple resolutions to mitigate spectral bias and explicitly model cross-scale dynamics. We demonstrate Triton's superior performance on challenging forecast tasks, achieving stable year-long global temperature forecasts, skillful Kuroshio eddy predictions till 120 days, and high-fidelity turbulence simulations preserving fine-scale structures all without external forcing, with significantly surpassing baseline AI models in long-term stability and accuracy. By effectively suppressing high-frequency error accumulation, Triton offers a promising pathway towards trustworthy AI-driven simulation for climate and earth system science.

Accelerating PDE Data Generation via Differential Operator Action in Solution Space

Recent advancements in data-driven approaches, such as Neural Operator (NO), have demonstrated their effectiveness in reducing the solving time of Partial Differential Equations (PDEs). However, one major challenge faced by these approaches is the requirement for a large amount of high-precision training data, which needs significant computational costs during the generation process. To address this challenge, we propose a novel PDE dataset generation algorithm, namely Differential Operator Action in Solution space (DiffOAS), which speeds up the data generation process and enhances the precision of the generated data simultaneously. Specifically, DiffOAS obtains a few basic PDE solutions and then combines them to get solutions. It applies differential operators on these solutions, a process we call 'operator action', to efficiently generate precise PDE data points. Theoretical analysis shows that the time complexity of DiffOAS method is one order lower than the existing generation method. Experimental results show that DiffOAS accelerates the generation of large-scale datasets with 10,000 instances by 300 times. Even with just 5% of the generation time, NO trained on the data generated by DiffOAS exhibits comparable performance to that using the existing generation method, which highlights the efficiency of DiffOAS.