Agentic Symbolic Search (ASYS) is a method that uses coding agents to build and refine explicit approximations of nonlinear partial differential equations (PDEs) by combining evolutionary search over differentiable symbolic programs with gradient-based fitting. ASYS evaluates candidate expressions using the governing PDE, guiding revisions toward more accurate representations. In applied tests, ASYS successfully inferred missing decay terms for a singular Constantin-Lax-Majda profile, reduced error in Fujita blow-up dynamics from 55.5% to 0.0879%, and produced a 14‑parameter mode‑coupling law for Allen‑Cahn interfaces that matches independent simulations.
By Zongmin Yu, Jun Zhai, Liu Yang
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
By Peng Yin, Kai Li, Yifan Zhang, Jian Cheng
arXiv:2509.06154v3 Announce Type: replace
Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings bet...
By Dibyajyoti Nayak, Somdatta Goswami
arXiv:2609.07437v1 Announce Type: cross
Abstract: Physics-informed neural networks (PINNs) represent a growing frontier in using artificial intelligence to solve partial differential equations (PDEs)...
By Xing Guo, Hongwei Tang, Zewei Meng, Yidong Zhang, Shaoqiu Xiao, Feng Liu
arXiv:2610.08475v1 Announce Type: new
Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
By Stefano Maria Pizzamiglio, Stefano Pagani, Francesco Regazzoni
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)
arXiv:2608. 04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem.
By Shengxin Kong, Liwen Xu, Jingwen Fu
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou
arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.
By Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban
arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis