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

Latest 50 papers on physics-informed neural networks: Dec. 27, 2025

Physics-Informed Neural Networks (PINNs) are rapidly transforming how we solve complex scientific and engineering problems. By embedding the fundamental laws of physics directly into neural network architectures and loss functions, PINNs offer a powerful alternative to traditional numerical methods, particularly for partial differential equations (PDEs), inverse problems, and real-time simulations. This exciting convergence of AI and physical sciences is pushing the boundaries of what’s possible, as evidenced by a recent surge of innovative research.

The Big Idea(s) & Core Innovations

Recent advancements in PINNs are primarily driven by efforts to enhance their accuracy, robustness, efficiency, and applicability to more challenging problems. A key theme across many papers is tackling the inherent difficulties of PINNs, such as spectral bias, handling discontinuities, and enforcing boundary conditions.

For instance, the Alternating Easy-Hard PINN (AEH-PINN) method, proposed by Zhaoqian Gao and Min Yang from the School of Mathematics and Information Sciences, Yantai University, in their paper “More Consistent Accuracy PINN via Alternating Easy-Hard Training”, introduces a hybrid training strategy that dynamically balances sample difficulty. This significantly improves accuracy, achieving relative L2 errors as low as O(10⁻⁵) to O(10⁻⁶) across diverse PDEs. Complementing this, the paper “FG-PINNs: A neural network method for solving nonhomogeneous PDEs with high frequency components” by J. Zheng et al. addresses spectral bias by using dual subnetworks to handle high- and low-frequency components separately, demonstrating superior convergence.

Another significant area of innovation lies in improving PINN architectures and training dynamics. Researchers from the University of Paris-Saclay, France, in “A Control Perspective on Training PINNs”, reinterpret PINN optimization as a control-affine system, introducing integral and leaky-integral controllers for enhanced stability and robustness, especially with noisy data or model mismatch. This theoretical underpinning is echoed by “A new initialisation to Control Gradients in Sinusoidal Neural network” by Andrea Combette et al. (ENSL, CNRS UMR 5672 Lyon), which proposes a novel initialization strategy for sinusoidal networks (like SIREN) to control gradients and prevent spectral bias, leading to improved generalization. Furthermore, Taeyoung Kim and Myungjoo Kang (Korea Institute for Advanced Study, Seoul National University) in “Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Field Theory Perspective” introduce MRePU, a modified activation function that ensures stable training and accurate derivative approximation, crucial for PINN applications.

Addressing complex boundary conditions and discontinuities is also a major focus. The paper “Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries” by Conor Rowan et al. (Smead Aerospace Engineering Sciences, University of Colorado Boulder) recommends using the strong form loss due to its generality for complex 3D geometries. Similarly, Xinjie He and Chenggong Zhang (University of California, Los Angeles) extend the Time-Evolving Natural Gradient (TENG) framework in “TENG++: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets under General Boundary Conditions” to support general boundary conditions with penalty terms, improving accuracy and stability. For highly discontinuous problems, Saif Ur Rehman and Wajid Yousuf’s “Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media (XPINN)” dynamically partitions the domain and uses localized subnetworks to resolve steep gradients without artificial diffusion.

Several papers also innovate on the core architecture for improved performance and efficiency. For example, Mohammad E. Heravifard and Kazem Hejranfar (Sharif University of Technology) introduce HWF-PIKAN in “HWF-PIKAN: A Multi-Resolution Hybrid Wavelet-Fourier Physics-Informed Kolmogorov-Arnold Network for solving Collisionless Boltzmann Equation”, combining wavelet and Fourier features for multi-scale representation and spectral bias mitigation, showing superior accuracy in high-dimensional phase-space dynamics. Shao-Ting Chiu et al. (Texas A&M University) present BumpNet in “BumpNet: A Sparse Neural Network Framework for Learning PDE Solutions”, a sparse framework that achieves h-adaptivity through pruning, concentrating basis functions in high-gradient regions for efficiency and accuracy. Moreover, Julian Evan Chrisnanto et al. propose ASPEN in “ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics”, which uses an adaptive spectral layer with learnable Fourier features to dynamically tune frequency representation, resolving multi-scale dynamics with exceptional accuracy.

Beyond PDEs, PINNs are being adapted for stochastic systems and complex imaging. Marek Baranek (AGH University of Krakow) introduces SPINNs in “SPINNs – Deep learning framework for approximation of stochastic differential equations” for solving SDEs. Mengxue Zhang et al. (Xiamen University, Fudan University) apply PINNs to medical imaging in “Error Bound Analysis of Physics-Informed Neural Networks-Driven T2 Quantification in Cardiac Magnetic Resonance Imaging”, enabling T2 quantification in cardiac MRI without ground-truth data, complete with rigorous error bounds.

Under the Hood: Models, Datasets, & Benchmarks

The innovations highlighted above are often built upon or validated by specific models, datasets, and benchmarks:

• AEH-PINN: Demonstrates improved accuracy across various partial differential equations, achieving relative L2 errors of O(10⁻⁵) to O(10⁻⁶). Code available at https://github.com/Gao-ST/PINN-Alternating-Easy-Hard.
• BumpNet: A flexible sparse neural network framework for PDE solutions, utilizing pruning for h-adaptivity. Code available at https://github.com/stchiu/BumpNet.
• TENG++: An extension of the Time-Evolving Natural Gradient framework for PDEs with general boundary conditions, showcasing superior accuracy with the Heun method. Resource: https://arxiv.org/abs/2512.15771.
• KD-PINN: A knowledge-distilled PINN framework for low-latency PDE solvers, achieving up to 6.9x speedup on Navier-Stokes equations with minimal accuracy loss. Code available at https://github.com/kbounja/KD-PINN.
• HWF-PIKAN: A hybrid Wavelet-Fourier Physics-Informed Kolmogorov-Arnold Network for solving the Collisionless Boltzmann Equation and other PDEs, excelling in multi-scale representation. Code available at https://github.com/m-heravifard/HWF-PIKAN.
• SAFE-NET: A feature engineering framework for PINNs that leverages Fourier features for faster and more stable convergence with significantly fewer parameters. Code available at https://github.com/jmclong/random.
• HeatTransFormer: A physics-guided Transformer architecture for interfacial heat conduction in semiconductor devices, enabling inverse identification of thermal properties. Code available at https://github.com/manicsetsuna/heattransformer.
• iPINNER: Integrates multi-objective optimization (NSGA-III) and ensemble Kalman filter (EnKF) for robust PINN performance with noisy data and incomplete physics. Resource: https://arxiv.org/pdf/2506.00731.
• DAE-HardNet: Enforces differential-algebraic (DAE) hard constraints using a differentiable projection layer based on KKT conditions. Code available at https://github.com/SOULS-TAMU/DAE-HardNet.
• IG-PINNs: Incorporates interface information into network structures via a gating mechanism for elliptic interface problems. Code available at https://github.com/jczheng126/Interface-gated-PINNs.
• RRaPINNs: Addresses tail residuals in PDE solutions using risk-aware optimization techniques like CVaR and Mean-Excess penalties. Code available at https://github.com/RRaPINNs.
• WbAR: A white-box adversarial attack refinement strategy for localizing and adaptively refining failure regions in PINNs. Code available at https://github.com/yaoli90/WbAR.
• QCPINNs: Quantum-Classical Physics-Informed Neural Networks for reservoir seepage equations, demonstrating improved accuracy and efficiency through hybrid quantum-classical approaches. Resource: https://arxiv.org/pdf/2512.03923.
• WPIQNN: Wavelet-Accelerated Physics-Informed Quantum Neural Network, which solves multiscale PDEs without automatic differentiation. Resource: https://arxiv.org/pdf/2512.08256.
• FBKANs and HPKM-PINN: Domain decomposition methods for Kolmogorov-Arnold Networks (KANs) and hybrid KAN/MLP architectures, improving accuracy and efficiency for multiscale problems. FBKANs code: https://github.com/pnnl/neuromancer/tree/feature/fbkans/examples/KANs.

Impact & The Road Ahead

These collective advancements significantly broaden the applicability and reliability of PINNs across diverse scientific and engineering domains. From medical imaging and cardiac biomechanics (“On Parameter Identification in Three-Dimensional Elasticity and Discretisation with Physics-Informed Neural Networks” by Federica Caforio et al. from the University of Graz) to atmospheric dispersion modeling (“Physics-Informed Neural Networks for Source Inversion and Parameters Estimation in Atmospheric Dispersion” by Brenda Anague et al. from the University of KwaZulu-Natal), PINNs are proving to be powerful tools for solving complex inverse problems with sparse data.

In critical infrastructure, PINNs are enhancing real-time control, as seen in the superior fault tolerance of PINNs over LSTMs for steam temperature control in power plants (“PINN vs LSTM: A Comparative Study for Steam Temperature Control in Heat Recovery Steam Generators” and “Fault-Tolerant Temperature Control of HRSG Superheaters: Stability Analysis Under Valve Leakage Using Physics-Informed Neural Networks” by Mojtaba Fanoodi et al., AmirKabir University of Technology). They are also accelerating electromagnetic transient stability assessment in power systems (“Scalable Physics-Informed Neural Networks for Accelerating Electromagnetic Transient Stability Assessment” by I. Ventura et al., DTU Computing Center).

The advent of quantum-classical PINNs (“Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations” by Rao, X. et al.) and wavelet-accelerated quantum neural networks (“Wavelet-Accelerated Physics-Informed Quantum Neural Network for Multiscale Partial Differential Equations” by D. Gupta et al., Indian Institute of Science) hints at a future where hybrid computing paradigms unlock even greater efficiency and accuracy for multiscale and high-dimensional problems.

Looking ahead, the emphasis will be on developing more robust, interpretable, and efficient PINN frameworks. Techniques like knowledge distillation (“KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers” by Karim Bounja et al., Hassan 1st University of Settat) and improved optimization strategies (“Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Loss” by Max Hirsch and Federico Pichi) will be crucial for real-time applications in robotics (“NeuroHJR: Hamilton-Jacobi Reachability-based Obstacle Avoidance in Complex Environments with Physics-Informed Neural Networks” by Granthik Halder et al., IISER Kolkata) and soft robotics (“Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks” by Author A et al.). Moreover, incorporating hard constraints (“DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraints” by Rahul Golder et al., Texas A&M University) and domain decomposition methods will enable PINNs to handle even more complex physical phenomena with greater fidelity. The journey of PINNs from a theoretical concept to a practical, indispensable tool in scientific computing is truly exciting, promising breakthroughs in fields from climate modeling to advanced materials science.