Physics-Informed Neural Networks: Unlocking Next-Gen Scientific Discovery and Real-World Applications

Latest 50 papers on physics-informed neural networks: Sep. 8, 2025

Physics-Informed Neural Networks (PINNs) are rapidly transforming how we model and solve complex scientific and engineering problems. By embedding the fundamental laws of physics directly into neural network architectures, PINNs promise to bridge the gap between data-driven machine learning and established scientific principles. Recent research showcases a burgeoning field, moving beyond foundational concepts to tackle deep theoretical challenges, enhance robustness, and unlock practical applications from medical diagnostics to advanced materials science and intelligent transportation.

The Big Idea(s) & Core Innovations

The central challenge PINNs address is solving complex Partial Differential Equations (PDEs) and inverse problems, often with scarce or noisy data, while ensuring physical consistency. Several recent papers present groundbreaking advancements:

• Robustness and Stability: A unified theoretical framework by Ronald Katende et al. from Kabale and Makerere Universities, in their paper “Non-Asymptotic Stability and Consistency Guarantees for Physics-Informed Neural Networks via Coercive Operator Analysis”, provides non-asymptotic bounds on PINN convergence and robustness. This work formally guarantees PINN stability through coercive operator analysis, addressing a critical theoretical gap. Similarly, Feilong Jiang et al. from Lancaster University and the University of Western Ontario introduce “Mask-PINNs: Mitigating Internal Covariate Shift in Physics-Informed Neural Networks”, a novel architecture using a learnable mask function to regulate feature distributions, greatly improving accuracy and training stability by mitigating internal covariate shift.

• Efficiency and Accuracy in PDE Solving: To accelerate complex PDE solutions, Xiong Xiong et al. from Northwestern Polytechnical University propose “Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs”. SV-SNN significantly improves accuracy for high-frequency PDEs by tackling spectral bias with variable separation and adaptive frequency learning. Another crucial advance in temporal accuracy comes from Xun Yang et al. at Sichuan Normal University with “D3PINNs: A Novel Physics-Informed Neural Network Framework for Staged Solving of Time-Dependent Partial Differential Equations”, which dynamically converts time-dependent PDEs into ODEs using domain decomposition. For handling sharp discontinuities in hyperbolic conservation laws, Yan Shen et al. from the University of Science and Technology of China introduce a “Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning”, blending DG discretizations with neural networks and progressive training.

• Smart Sampling and Optimization: Adaptive sampling strategies are key to efficiency. Weihang Ouyang et al. from Hong Kong Polytechnic University and Yale University introduce “RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations”, using adversarial gradients to optimize sample placement and improve accuracy without increasing collocation points. In a similar vein, Qinjiao Gao et al. from Zhejiang Gongshang University propose “Energy-Equidistributed Moving Sampling Physics-informed Neural Networks for Solving Conservative Partial Differential Equations” (EEMS-PINNs), ensuring energy conservation through dynamic mesh adaptation. Complementing these are advancements in optimizers: Stavros Kassinos from the University of Cyprus introduces “Kourkoutas-Beta: A Sunspike-Driven Adam Optimizer with Desert Flair”, an Adam variant that dynamically adjusts based on gradient spikes for improved stability in PDE surrogates. Furthermore, Elham Kiyania et al. at Brown University, in “Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks”, show that advanced quasi-Newton methods dramatically enhance PINN training efficiency.

• Novel Architectures and Constraints: The field is seeing innovative architectural shifts. Yanpeng Gong et al. from Beijing University of Technology introduce “Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging” (PIKAN), leveraging KANs to handle material discontinuities without domain decomposition. For enforcing strict physical constraints, Ashfaq Iftakher et al. from Texas A&M University develop “Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints” (KKT-Hardnet), ensuring physical consistency through differentiable projection layers. In a significant leap, Afrah Farea et al. from Istanbul Technical University introduce “QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs”, a hybrid quantum-classical model that achieves comparable accuracy to classical PINNs with significantly fewer parameters.

Under the Hood: Models, Datasets, & Benchmarks

These innovations are powered by new models, datasets, and refined benchmarks:

• PinnDE Library: Jason Matthews and Alex Bihlo from Memorial University of Newfoundland introduce “PinnDE: Physics-Informed Neural Networks for Solving Differential Equations”, an open-source Python library integrating PINNs and DeepONets for user-friendly differential equation solving.
• PINNMamba: Chenhui Xu et al. from the University at Buffalo propose “Sub-Sequential Physics-Informed Learning with State Space Model”, an SSM-based framework addressing PINN failure modes and over-smoothing, achieving state-of-the-art results on multiple PDE benchmarks.
• JacobiNet: For complex geometries, X. C. et al. introduce “Solved in Unit Domain: JacobiNet for Differentiable Coordinate Transformations”, a network that learns continuous, differentiable mappings from irregular physical domains to regular reference spaces, seamlessly integrating with PINNs.
• BubbleONet: Yunhao Zhang et al. from Worcester Polytechnic Institute introduce “BubbleONet: A Physics-Informed Neural Operator for High-Frequency Bubble Dynamics”, which uses the Rowdy adaptive activation function and two-step training to accurately simulate high-frequency bubble dynamics, built on the PI-DeepONet framework.
• Code Repositories for Optimizers: Jonas Søeborg Nielsen et al. provide code for their “Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models” framework, offering a faster alternative to PINNs for parameter estimation. Similarly, WenBo’s “Overcoming the Loss Conditioning Bottleneck in Optimization-Based PDE Solvers: A Novel Well-Conditioned Loss Function” provides a Stabilized Gradient Residual (SGR) loss function, and Tianchen Song et al. introduce “A matrix preconditioning framework for physics-informed neural networks based on adjoint method” for improved PINN convergence.

Impact & The Road Ahead

The impact of these advancements spans a wide range of fields. In medical imaging, “Towards Digital Twins for Optimal Radioembolization” by P. Abbeel et al. from Stanford University and other institutions, utilizes digital twins for personalized cancer treatment, demonstrating how real-time simulation can enhance precision. “Estimation of Hemodynamic Parameters via Physics Informed Neural Networks including Hematocrit Dependent Rheology” by Moises Sierpea et al. at Universidad de Santiago de Chile, highlights PINNs’ ability to accurately estimate blood flow parameters from 4D-flow MRI data, potentially revolutionizing cardiovascular diagnostics.

For intelligent transportation systems, “Physics-informed deep operator network for traffic state estimation” by Zhihao Li et al. at Tongji University introduces PI-DeepONet for superior traffic state estimation, while “Generalising Traffic Forecasting to Regions without Traffic Observations” by Xinyu Su et al. at the University of Melbourne presents GenCast, a model that integrates physics and external signals to forecast traffic in unobserved regions. In materials science, “Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding” by Jan A. Zak at the University of Augsburg shows how PINNs can enhance predictive modeling for complex industrial processes.

These papers collectively paint a picture of a rapidly maturing field, addressing core limitations while pushing the boundaries of applicability. The road ahead involves further integrating these theoretical advancements into practical, scalable solutions, particularly for complex multi-physics systems, and expanding the rigorous error certification frameworks for greater reliability. As PINNs continue to evolve with smarter architectures, adaptive training, and robust theoretical underpinnings, they are poised to become indispensable tools for scientific discovery and real-world problem-solving across countless domains.