Physics-Informed Neural Networks: Unlocking Deeper Physics, Faster Solutions, and Smarter AI

Latest 50 papers on physics-informed neural networks: Oct. 12, 2025

Physics-InInformed Neural Networks (PINNs) have emerged as a powerful paradigm, fusing the expressiveness of deep learning with the foundational rigor of physical laws. They promise to revolutionize scientific discovery, engineering, and real-world applications by embedding domain knowledge directly into neural network architectures. This fascinating field is rapidly evolving, tackling challenges from complex system modeling to achieving computational efficiency. Let’s dive into some of the latest breakthroughs that showcase the incredible progress and future potential of PINNs.

The Big Idea(s) & Core Innovations

The recent surge in PINN research highlights a dual focus: enhancing the models’ physical fidelity and interpretability while simultaneously boosting their computational efficiency and robustness. Many papers are exploring how to make PINNs more physically sound and reliable, particularly when dealing with complex or noisy data.

For instance, the groundbreaking work by Javier Castro and Benjamin Gess from Technische Universität Berlin and Max Planck Institute for Mathematics in the Sciences introduces THINNs: Thermodynamically Informed Neural Networks. They propose replacing the arbitrary L2-norm penalization in PINNs with a thermodynamically consistent rate functional derived from large deviation principles. This approach ensures more robust and accurate solutions, especially for non-equilibrium fluctuating systems and problems with discontinuities, like shock formation in the viscous Burgers’ equation.

Adding another layer of physical rigor, Kim Bente et al. from the University of Sydney in their paper, Mass Conservation on Rails – Rethinking Physics-Informed Learning of Ice Flow Vector Fields, introduce divergence-free neural networks (dfNNs). These models enforce exact mass conservation, providing more reliable estimates for ice flow modeling than traditional PINNs and unconstrained neural networks. Their directional guidance strategy further leverages satellite data to enhance performance, demonstrating the importance of hard physical constraints.

Meanwhile, efforts are underway to make PINNs more adaptable and interpretable across various scientific domains. Yunpeng Gong et al. from Xiamen University present StruSR: Structure-Aware Symbolic Regression with Physics-Informed Taylor Guidance. This framework leverages local Taylor expansions from trained PINNs as derivative-based priors to guide symbolic regression, yielding interpretable mathematical expressions that are both physically consistent and structurally faithful. Similarly, Kürsat Tekbıyık and Anil Gurses from Bilkent University propose PIKAN: Physics-Inspired Kolmogorov-Arnold Networks for Explainable UAV Channel Modelling, integrating physical principles into the Kolmogorov-Arnold network structure to achieve explainable and accurate prediction of air-to-ground (A2G) channels.

On the efficiency front, several innovations are pushing the boundaries of PINN training. Chinmay Datar et al. from the Technical University of Munich, Delft University of Technology, and Eindhoven University of Technology introduce Fast training of accurate physics-informed neural networks without gradient descent. Their Frozen-PINN method achieves staggering speedups—up to 100,000x faster—by eliminating gradient descent and using space-time separation with random features. This not only accelerates training but also enforces temporal causality. Complementing this, Kang An et al. from Rice University and The Chinese University of Hong Kong, Shenzhen, address optimization stability with AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networks. By employing independent optimizers for each loss component, AutoBalance tackles the challenge of balancing multiple loss terms, improving stability and performance in solving PDEs.

Under the Hood: Models, Datasets, & Benchmarks

These advancements are often powered by novel architectures, sophisticated optimization strategies, and robust benchmarking. Here are some key resources and models highlighted:

• Frozen-PINN: This novel training algorithm from Chinmay Datar et al. bypasses gradient descent for solving time-dependent PDEs, offering extreme speedups. Code is available at https://gitlab.com/felix.dietrich/swimpde-paper.git.
• AutoBalance: Developed by Kang An et al., this framework employs a ‘post-combine’ approach with independent optimizers per loss term, enhancing PINN stability and performance on PDE benchmarks. (Code not explicitly provided, but insights are broadly applicable).
• S-Pformer (Spectral PINNSformer): Introduced by Rohan Arni and Carlos Blanco from High Technology High School and The Pennsylvania State University/Princeton University in Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decoding, this encoder-free Transformer-based PINN uses Fourier features and attention to mitigate spectral bias, outperforming traditional MLPs with fewer parameters.
• Lang-PINN: From Xin He et al. at A*STAR, Hong Kong Baptist University, and North China Electric Power University, Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework is an LLM-driven multi-agent system that automatically generates PINN solutions from natural language. It includes a benchmark dataset for systematic evaluation. (Code references other projects).
• RBF-PIELM: Akshay Govind Srinivasan et al. from Indian Institute of Technology Madras and Creatis Biomedical Imaging Laboratory benchmark this shallow, physics-informed extreme learning machine variant in Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation, demonstrating faster training and lower parameter count than deep PINNs. They also extend PIELMs for finance in Towards Fast Option Pricing PDE Solvers Powered by PIELM, providing a codebase at https://anonymous.4open.science/r/PIELM-for-Option-Pricing-66CB.
• PACMANN (Point Adaptive Collocation Method for Artificial Neural Networks): Coen Visser et al. from Delft University of Technology developed this adaptive sampling method for PINNs, which dynamically adjusts collocation points based on residual gradients to improve accuracy and efficiency in high-dimensional PDEs. Code is available at https://github.com/CoenVisser/PACMANN.
• AW-EL-PINNs: Chuandong Li and Runtian Zeng from Southwest University introduce this multi-task learning framework in AW-EL-PINNs: A Multi-Task Learning Physics-Informed Neural Network for Euler-Lagrange Systems in Optimal Control Problems, enhancing PINN performance for optimal control problems with adaptive loss weighting.
• Nyström-Accelerated Primal LS-SVMs: Weikuo Wang et al. from China Three Gorges University, in their paper Nyström-Accelerated Primal LS-SVMs: Breaking the O(an³) Complexity Bottleneck for Scalable ODEs Learning, present a framework for ODE solving that reduces computational complexity from O(an³) to O((m + p)³), with code at https://github.com/AI4SciCompLab/NLS-SVMs.
• ReBaNO (Reduced Basis Neural Operator): Haolan Zheng et al. from the University of Massachusetts Dartmouth introduce ReBaNO in ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance, a data-lean operator learning algorithm that ensures discretization invariance and reduces generalization gaps, with code at https://github.com/haolanzheng/rebano.

Impact & The Road Ahead

The impact of these advancements is profound and far-reaching. From epidemiological modeling of COVID-19 dynamics in German states by P. Rothenbeck et al. (Modeling COVID-19 Dynamics in German States Using Physics-Informed Neural Networks) to solving complex integral equations with Mahdi Movahedian Moghaddam et al.’s Advanced Physics-Informed Neural Network with Residuals for Solving Complex Integral Equations, PINNs are proving their versatility. We’re seeing them deployed in biomedical science and engineering, as reviewed by Nazanin Ahmadi et al. from Brown and Yale Universities in Physics-Informed Machine Learning in Biomedical Science and Engineering, enabling accurate and interpretable predictions in biomechanics, pharmacokinetics, and medical imaging.

The integration of large language models with PINNs, as seen in Lang-PINN and the SciML Agents framework by Saarth Gaonkar et al. from UC Berkeley and LBNL (SciML Agents: Write the Solver, Not the Solution), hints at a future where scientific modeling can be automated from natural language descriptions. This bridging of scientific intent and executable models promises to democratize complex simulations.

Challenges remain, particularly concerning robustness to noise in inverse problems, as highlighted by Aleksandra Jekica et al. from the Norwegian University of Science and Technology in Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems. However, new approaches like AW-EL-PINNs for optimal control by Chuandong Li and Runtian Zeng (AW-EL-PINNs: A Multi-Task Learning Physics-Informed Neural Network for Euler-Lagrange Systems in Optimal Control Problems), or the rigorous error analysis of PINNs for Boltzmann equation by E. Abdo et al. from UC Santa Barbara (Error estimates of physics-informed neural networks for approximating Boltzmann equation) are laying the theoretical and practical groundwork for overcoming these hurdles. Furthermore, methods like the self-adaptive weighting from Wenqian Chen et al. at Pacific Northwest National Laboratory (Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks) and AutoBalance are crucial for stabilizing training and improving accuracy.

From modeling quantum noise tomography by Antonin Sulc from Lawrence Berkeley National Lab (Quantum Noise Tomography with Physics-Informed Neural Networks) to continuous-time multi-agent reinforcement learning by Xuefeng Wang et al. from Purdue University (Continuous-Time Value Iteration for Multi-Agent Reinforcement Learning), PINNs are expanding into new frontiers. The collective research points to a future where PINNs are not just solving equations, but also accelerating scientific discovery, making AI more interpretable, and enabling robust solutions across an ever-growing spectrum of complex problems. The journey of physics-informed AI is truly exciting, promising smarter, faster, and more reliable scientific computing.