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.
arXiv:2606. 20467v1 Announce Type: new Abstract: Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values.
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.
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.
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:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
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.
arXiv:2608. 04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem.
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv:2609.23023v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) require coordinated choices over network representation, sampling, loss construction, and optimization, while...
arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
arXiv:2603.27936v3 Announce Type: replace-cross Abstract: Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Netw...