The paper introduces SED-MCTS, a Monte Carlo tree search method that enhances PDE solution discovery by distilling structural experience from evaluated expressions. Unlike previous approaches that rely on a single terminal score, SED-MCTS uses counterfactual subtree interventions to estimate local structural contributions, guiding the search toward reliable construction edges and preserving useful components in a structural archive. The method extends naturally to coupled multiphysics systems and demonstrates improved performance, efficiency, and robustness across diverse PDE benchmarks, especially under noisy or scarce observations.
arXiv:2610.26963v1 Announce Type: cross Abstract: Discovering governing partial differential equations (PDEs) from observed data is a central inverse problem in computational science and engineering:...
arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.
arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.
arXiv:2606. 30699v1 Announce Type: new Abstract: Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning.
arXiv:2608.22504v1 Announce Type: new Abstract: Existing AI-for-PDE benchmarks primarily assess models in terms of predictive or approximation accuracy. In physics research, however, AI outputs often...
The paper presents a probabilistic symbolic regression framework that models mathematical expressions as ensembles of symbolic trees, using a regularizing prior to control complexity and an Occam’s window-based posterior to capture uncertainty across plausible models. It provides theoretical guarantees on posterior concentration, including near‑parametric rates when an exact finite formula exists and oracle results under misspecification. Empirical results show the method outperforms state‑of‑the‑art competitors in predictive accuracy, symbolic complexity, and structural recovery on benchmark scientific equations and a materials discovery task.
SCICONVBENCH is a benchmark designed to evaluate large language models (LLMs) on multi‑turn clarification tasks in computational science. It focuses on two key abilities: eliciting missing information (disambiguation) and resolving contradictory requests (inconsistency resolution) across four domains—fluid mechanics, solid mechanics, materials science, and partial differential equations. The benchmark pairs a structured task ontology with a rubric‑based evaluation framework, measuring LLM performance in clarification behavior, conversational grounding, and final‑specification fidelity, and reveals that even top models only resolve about 52.7% of disambiguation cases in fluid mechanics while often making ungrounded assumptions.
arXiv:2606. 05191v1 Announce Type: new Abstract: Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements.
The paper introduces HER-PDE, a scientific-agent framework that simultaneously discovers partial differential equation (PDE) structures and their unknown spatial coefficient fields. Using two noisy trajectories from different excitations, the agent generates expression-tree hypotheses, evaluates them via a Hypothesis Evaluation Interface that only estimates declared fields, and refines candidates through bidirectional cross-excitation transfer. In controlled experiments on five two-dimensional systems with Gaussian noise, HER-PDE accurately recovers the governing operators and attains a median Pearson correlation of ~0.85 and a median relative L2 error of ~0.28 for nine unknown coefficient fields.
arXiv:2606. 25039v1 Announce Type: new Abstract: Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains.
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.