Physics-Informed Neural Networks: Unlocking Next-Gen Scientific Computing

Latest 50 papers on physics-informed neural networks: Sep. 1, 2025

Physics-Informed Neural Networks (PINNs) are rapidly transforming how we approach scientific computing, offering a powerful blend of data-driven learning and fundamental physical laws. While traditional numerical methods often struggle with complex geometries, high-dimensional spaces, or sparse data, PINNs present a versatile alternative capable of solving differential equations, estimating parameters, and even discovering new physical insights. Recent research has pushed the boundaries of PINNs, addressing critical challenges in accuracy, stability, computational efficiency, and theoretical understanding. This blog post dives into some of the most exciting breakthroughs, revealing how these innovations are setting the stage for a new era of scientific discovery.

The Big Idea(s) & Core Innovations

The central theme across recent papers is the continuous drive to make PINNs more robust, accurate, and versatile. A key challenge lies in accurately solving time-dependent and high-frequency Partial Differential Equations (PDEs). Researchers at the School of Mathematical Sciences, Sichuan Normal University, in their paper “D3PINNs: A Novel Physics-Informed Neural Network Framework for Staged Solving of Time-Dependent Partial Differential Equations”, introduce D3PINNs, which dynamically convert time-dependent PDEs into ODEs using domain decomposition. This preserves PINN efficiency while significantly enhancing temporal accuracy. Similarly, “PIANO: Physics Informed Autoregressive Network” by Mayank Nagda and colleagues from RPTU Kaiserslautern-Landau tackles temporal instability by introducing an autoregressive framework, conditioning predictions on prior states for stable propagation of physical dynamics.

For high-frequency problems, which often suffer from spectral bias, “Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs” from Xiong Xiong and his team at Northwestern Polytechnical University proposes SV-SNN, integrating variable separation with adaptive spectral features to achieve 1-3 orders of magnitude improvement in accuracy. Building on this, “Spectral-Prior Guided Multistage Physics-Informed Neural Networks for Highly Accurate PDE Solutions” by Yuzhen Li and colleagues further enhances PINN accuracy by using spectral information to guide network initialization and incorporate Random Fourier Features, particularly effective for high-energy physical modes.

Another critical area of innovation is handling complex geometries and constraints. “Solved in Unit Domain: JacobiNet for Differentiable Coordinate Transformations” introduces JacobiNet, a neural network that learns differentiable mappings from irregular physical domains to regular reference spaces, enabling PINNs to tackle complex geometries without manual PDE reformulation. Addressing strict physical constraints, Ashfaq Iftakher and the team from Texas A&M University introduce KKT-Hardnet+ in “Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints”, a PINN architecture that enforces strict nonlinear equality and inequality constraints through differentiable projection layers, ensuring physical consistency.

Beyond direct PDE solving, PINNs are being adapted for diverse applications. “Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models” by Jonas Søeborg Nielsen and colleagues from the Technical University of Denmark proposes Physics-Informed Regression (PIR), demonstrating faster and more accurate parameter estimation for nonlinear dynamic models compared to traditional PINNs. In materials science, “Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding” by Jan A. Zak from the University of Augsburg, integrates real experimental data with PINNs to improve predictive capabilities for aluminum spot welding, showcasing practical industrial impact.

Under the Hood: Models, Datasets, & Benchmarks

Recent advancements in PINNs are often underpinned by novel architectural designs, optimized training strategies, and robust data utilization:

• Novel Architectures:
  • QCPINN in “QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs” by Afrah Farea and co-authors introduces a hybrid quantum-classical neural network that achieves comparable accuracy to classical PINNs with significantly fewer parameters (around 10%). This points to potential quantum advantage in parameter efficiency.
  • PIKAN in “Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging” from Yanpeng Gong and his team replaces traditional MLPs with Kolmogorov-Arnold Networks (KANs), leveraging trainable B-spline activation functions to naturally handle material discontinuities without domain decomposition.
  • LNN–PINN from Ze Tao and others in “LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks” integrates liquid residual gating into PINNs, enhancing predictive accuracy in physics-only training scenarios.
  • BubbleONet from Yunhao Zhang, Lin Cheng, and their colleagues in “BubbleONet: A Physics-Informed Neural Operator for High-Frequency Bubble Dynamics” uses a PI-DeepONet framework with the Rowdy adaptive activation function to mitigate spectral bias in high-frequency bubble dynamics simulations.
  • PVD-ONet by Tiantian Sun and Jian Zu from Northeast Normal University in “PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems” leverages the Van Dyke matching principle within a DeepONet for multi-scale boundary layer problems.
  • Hybrid Fourier-Neural Architecture in “Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy” by Wei Shan Lee and his team achieves unprecedented L2 error for the Euler-Bernoulli beam equation by combining truncated Fourier series with deep neural networks.
• Optimization & Training Strategies:
  • “Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks” by Elham Kiyania et al. explores quasi-Newton methods like SSBFGS and SSBroyden to improve PINN and PIKAN training, achieving state-of-the-art results without adaptive weights.
  • “Kourkoutas-Beta: A Sunspike-Driven Adam Optimizer with Desert Flair” by Stavros Kassinos introduces an Adam variant (Kourkoutas-β) that dynamically adjusts its second-moment discount based on gradient spikes, improving stability and performance for bursty gradients common in PDE surrogates.
  • “Regime-Aware Time Weighting for Physics-Informed Neural Networks” by Gabriel Turinici uses Lyapunov exponents to adaptively adjust time weights, improving convergence and accuracy in chaotic and stable systems.
  • “Overcoming the Loss Conditioning Bottleneck in Optimization-Based PDE Solvers: A Novel Well-Conditioned Loss Function” proposes a Stabilized Gradient Residual (SGR) loss to tackle ill-conditioning in PDE solvers, significantly accelerating convergence.
  • “A matrix preconditioning framework for physics-informed neural networks based on adjoint method” by Tianchen Song and his team introduces Pre-PINNs, a matrix preconditioning approach to address ill-conditioning, enhancing convergence and stability for challenging multi-scale problems like Navier–Stokes equations.
  • “Improving Neural Network Training using Dynamic Learning Rate Schedule for PINNs and Image Classification” proposes a dynamic learning rate scheduler (DLRS) that adapts based on loss values, enhancing convergence and stability for PINNs and other NN tasks.
• Data & Sampling:
  • “Strategies for training point distributions in physics-informed neural networks” by Santosh Humagain and Toni Schneidereit investigates the impact of training point distribution, suggesting sine-based points inspired by Chebyshev nodes for improved accuracy.
  • “Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method” by Adrian Celaya, David Fuentes, and Beatrice Riviere introduces QR-DEIM based adaptive collocation strategies, outperforming fixed and other adaptive sampling techniques.
  • “Sub-Sequential Physics-Informed Learning with State Space Model” from Chenhui Xu et al. introduces PINNMamba, an SSM-based framework to address continuous-discrete mismatch and simplicity bias, significantly reducing over-smoothing and improving accuracy in PDEs.
• Tools & Libraries:
  • “PinnDE: Physics-Informed Neural Networks for Solving Differential Equations” by Jason Matthews and Alex Bihlo provides an open-source Python library for PINNs and DeepONets, simplifying the workflow for both forward and inverse problems.

Impact & The Road Ahead

These advancements in Physics-Informed Neural Networks herald a profound impact across scientific and engineering disciplines. From predicting intricate fluid dynamics in “Learning Fluid-Structure Interaction Dynamics with Physics-Informed Neural Networks and Immersed Boundary Methods” to precise hemodynamic parameter estimation in “Estimation of Hemodynamic Parameters via Physics Informed Neural Networks including Hematocrit Dependent Rheology”, PINNs are enabling unprecedented accuracy and efficiency in modeling complex real-world phenomena. In urban planning, “Physics-informed deep operator network for traffic state estimation” and “Generalising Traffic Forecasting to Regions without Traffic Observations” demonstrate how integrating physical laws can significantly improve traffic forecasting even in data-sparse regions.

Beyond solving existing problems, PINNs are evolving into tools for scientific discovery. The “Automated discovery of finite volume schemes using Graph Neural Networks” by Paul Garnier and his colleagues shows GNNs automatically rediscovering and generalizing numerical methods, even learning exact analytical forms. Similarly, “DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation” from Aniket Suryawanshi and his team combines neural networks with symbolic reasoning for interpretable scientific discovery in robotics.

However, challenges remain. “Challenges in automatic differentiation and numerical integration in physics-informed neural networks modelling” by Josef Daněk and Jan Pospíšil highlights critical precision issues in automatic differentiation and numerical integration, emphasizing the need for higher precision arithmetic. The theoretical underpinnings are also continually being refined, with papers like “A convergence framework for energy minimisation of linear self-adjoint elliptic PDEs in nonlinear approximation spaces” and “Optimization and generalization analysis for two-layer physics-informed neural networks without over-parametrization” providing rigorous convergence and generalization guarantees.

The future of PINNs is bright, with ongoing research pushing towards greater accuracy, efficiency, and broader applicability. The development of robust frameworks like “LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process” for uncertainty quantification, and adaptive approaches such as those in “Hybrid Adaptive Modeling in Process Monitoring: Leveraging Sequence Encoders and Physics-Informed Neural Networks”, points to increasingly sophisticated and reliable models. As these technologies mature, we can anticipate a paradigm shift in how we understand, predict, and control complex physical systems, accelerating scientific progress and unlocking solutions to some of humanity’s most pressing challenges.