Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields
YuJie HuangWenWu HeZhuoEr LinCongcong LiuDong LiangZhuo-Xu Cui
Aug 2026
Artificial IntelligenceMachine Learning
Abstract
Discovering PDEs in heterogeneous media requires jointly identifying the governing operator and the unknown spatial fields that parameterize it. These tasks are coupled: changing field placement changes the differential law, while a sufficiently flexible field can conceal structural error on a single trajectory. We present Hypothesize, Evaluate, Refine for PDE Discovery (HER-PDE), a scientific-agent framework that discovers compositional PDE structure together with nonparametric, time-invariant coefficient fields. The Agent analyzes two noisy trajectories generated by different excitations, proposes complete expression-tree hypotheses, and combines creative structural exploration with local candidate refinement. Its Hypothesis Evaluation Interface (HEI) estimates only the fields explicitly declared in each hypothesis, never adds missing terms, and scores structures by bidirectional cross-excitation transfer. The selected law is subsequently audited on a sealed temporal interval. Across five controlled two-dimensional systems observed with 5 percent relative Gaussian state noise, the Agent recovers the generating operator in all five cases, including equivalent signed-field and product-rule parameterizations. Across nine unknown coefficient fields, the recovered fields attain a median Pearson correlation of approximately 0.85 and a median relative L2 error of approximately 0.28. These results show that agent-guided hypothesis refinement can recover heterogeneous governing laws without prescribing a parametric form for their spatial coefficients.
This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-physics FFF simulation results into a deep neural network (DNN), thus ensuring consistency with physical laws: (1) incorporate physics constraints within the loss function of the DNN, (2) use physics model outputs as additional inputs to the DNN model, and (3) pre-train a DNN model with physics model input-output and then update it with experimental data. These strategies help to enforce a physically consistent relationship between bond quality and tensile strength, thus making porosity predictions physically meaningful. Eight different combinations of the above strategies are investigated. The results show how the combination of multiple strategies produces accurate machine learning models even with limited experimental data.
B. Kapusuzoglu, S. Mahadevan· JOM· 79 citations· ⚡2
This work introduces a pioneering exploration of Self-Supervised Learning (SSL) within the SNN, and proposes a novel Spiking Self-Attention (SSA) and Spiking Transformer (Spikformer) that achieves 80+% accuracy on ImageNet.
Zhaokun Zhou, Kaiwei Che, Wei Fang et al.· arXiv.org· 69 citations· ⚡10
This paper considers global sensitivity analysis (GSA) for situations where both a physics-based model and experimental observations are available, and investigates physics-informed machine learning strategies to effectively combine the two sources of information in order to maximize the accuracy of the sensitivity estimate.
B. Kapusuzoglu, S. Mahadevan· Reliability Engineering & Sy...· 45 citations
EquiPocket is proposed, an E(3)-equivariant Graph Neural Network for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms.
Yang Zhang, Wenbing Huang, Zhewei Wei et al.· International Conference on...· 43 citations· ⚡4
Investigating how experienced developers use agents in building software, including their motivations, strategies, task suitability, and sentiments finds that while experienced developers value agents as a productivity boost, they retain their agency in software design and implementation out of insistence on fundamental software quality attributes.
An adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs is developed that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model.
B. Kapusuzoglu, S. Mahadevan, Shunsaku Matsumoto et al.· Structural And Multidiscipli...· 17 citations
