Physics-Informed Neural Networks: Navigating New Frontiers from Quantum Noise to Digital Twins

Latest 50 papers on physics-informed neural networks: Oct. 6, 2025

Physics-Informed Neural Networks (PINNs) continue to be a vibrant and rapidly evolving field at the intersection of AI/ML and scientific computing. By embedding domain-specific physical laws directly into neural network loss functions, PINNs offer a powerful paradigm for solving complex scientific and engineering problems. Recent research has pushed the boundaries of PINNs, addressing critical challenges in efficiency, accuracy, robustness, and interpretability, while also expanding their application across diverse scientific domains. This blog post dives into some of the latest breakthroughs, synthesizing insights from cutting-edge papers that are redefining what’s possible with physics-informed AI.

The Big Idea(s) & Core Innovations

One of the central themes in recent PINN research is the drive for enhanced accuracy and efficiency, particularly for complex and high-dimensional systems. Traditional PINNs often struggle with training stability, convergence speed, and generalization, leading researchers to explore novel architectural and optimization strategies.

For instance, the paper “Fast training of accurate physics-informed neural networks without gradient descent” by Chinmay Datar et al. from the Technical University of Munich introduces Frozen-PINN, a groundbreaking approach that achieves up to 100,000x faster training times by eliminating gradient descent entirely. This is achieved through space-time separation and random features, enforcing temporal causality and drastically improving efficiency. Complementing this, Sifan Wang et al. from Yale University in “Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective” diagnose and resolve critical directional gradient conflicts in PINNs using a novel gradient alignment score. Their work demonstrates that second-order optimization methods like SOAP can lead to 2-10x accuracy improvements, even on challenging turbulent flows.

Another significant area of innovation lies in improving robustness and generalization, especially for real-world applications with noisy or sparse data. “A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networks” by Yifan Yu et al. from the National University of Singapore introduces a distribution-free conformal prediction framework for PINNs, providing rigorous statistical guarantees for uncertainty quantification, crucial for reliable scientific computing. Similarly, “AW-EL-PINNs: A Multi-Task Learning Physics-Informed Neural Network for Euler-Lagrange Systems in Optimal Control Problems” by Chuandong Li and Runtian Zeng from Southwest University tackles optimal control problems using adaptive loss weighting, achieving superior accuracy and stability for nonlinear systems by dynamically balancing loss components. Feilong Jiang et al. from Lancaster University address the internal covariate shift problem in “Mask-PINNs: Mitigating Internal Covariate Shift in Physics-Informed Neural Networks”, proposing a learnable mask function that regulates feature distributions while preserving physical constraints, leading to improved accuracy and stability in wider networks.

Specialized applications also see significant advancements. For instance, Khoa Tran et al. at AIWARE Limited Company present “SeqBattNet: A Discrete-State Physics-Informed Neural Network with Aging Adaptation for Battery Modeling”, which uses a discrete-state PINN with aging adaptation for highly accurate battery voltage prediction using minimal parameters. In the realm of high-energy physics, Katsuki Furuichi and Toshitaka Kuroda from RIKEN demonstrate PINNs’ versatility in “Physics-informed neural network solves minimal surfaces in curved spacetime”, tackling singularities and moving boundaries in Anti-de Sitter geometries. Antonin Sulc from Lawrence Berkeley National Lab applies PINNs to quantum computing in “Quantum Noise Tomography with Physics-Informed Neural Networks”, creating interpretable digital twins of noisy quantum systems from sparse data, enabling scalable quantum device characterization.

Under the Hood: Models, Datasets, & Benchmarks

The innovations highlighted above are often built upon or necessitate novel models, datasets, and benchmarks. This section outlines some key resources and architectural advancements:

• Gated X-TFC: Introduced by Vikas Dwivedi et al. (CREATIS Biomedical Imaging Laboratory, INSA) in “Gated X-TFC: Soft Domain Decomposition for Forward and Inverse Problems in Sharp-Gradient PDEs”, this framework uses differentiable logistic gates and an operator-conditioned meta-learning layer for efficient boundary layer resolution in sharp-gradient PDEs. Code is available at https://github.com/GatedX-TFC.
• Frozen-PINN: Developed by Chinmay Datar et al. (Technical University of Munich) in “Fast training of accurate physics-informed neural networks without gradient descent”, this model employs space-time separation and an SVD layer to achieve significant speedups without gradient descent. Code is available at https://gitlab.com/felix.dietrich/swimpde-paper.git.
• PACMANN: From Coen Visser et al. (Delft University of Technology) in “PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks”, this adaptive sampling method for PINNs dynamically moves collocation points based on residual gradients. The code is publicly accessible at https://github.com/CoenVisser/PACMANN.
• HyPINO: Presented by Rafael Bischof et al. (ETH Zurich) in “HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions”, this multi-physics neural operator leverages hypernetworks and mixed supervision for zero-shot generalization across PDEs.
• MasconCube: Pietro Fanti and Dario Izzo (ESA Advanced Concepts Team) introduced this self-supervised method for gravity inversion in “MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation”, using a 3D grid of point masses. Code can be found at https://github.com/esa/masconCube.
• PhyRMDM: In “Physics-Informed Representation Alignment for Sparse Radio-Map Reconstruction”, Haozhe Jia et al. (HKUST (GZ)) propose a dual U-Net architecture to enforce Helmholtz equation constraints for radio map reconstruction. Code is available (labeled as ‘Code’).
• RISN: Mahdi Movahedian Moghaddam et al. (Shahid Beheshti University) introduce RISN in “Advanced Physics-Informed Neural Network with Residuals for Solving Complex Integral Equations” to solve integral equations using residual connections and high-accuracy numerical methods.
• ODE-1000 Benchmark: Introduced by Saarth Gaonkar et al. (UC Berkeley) in “SciML Agents: Write the Solver, Not the Solution”, this dataset evaluates LLMs’ ability to generate scientifically appropriate code for ODE solvers. The code repository is https://github.com/SqueezeAILab/sciml-agent.
• D3PINNs: Xun Yang et al. (Sichuan Normal University) in “D3PINNs: A Novel Physics-Informed Neural Network Framework for Staged Solving of Time-Dependent Partial Differential Equations” propose a framework integrating PINNs with domain decomposition and numerical methods to dynamically convert PDEs into ODEs.
• EEMS-PINNs: From Qinjiao Gao et al. (Zhejiang Gongshang University), “Energy-Equidistributed Moving Sampling Physics-informed Neural Networks for Solving Conservative Partial Differential Equations” introduces adaptive mesh optimization based on energy density functions to ensure energy conservation in long-time simulations. Code is available at https://github.com/sufe-Ran-Zhang/EMMPDE.
• ReBaNO: Haolan Zheng et al. (University of Massachusetts Dartmouth) introduce ReBaNO in “ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance” as a data-lean operator learning algorithm that achieves discretization invariance. Code is available at https://github.com/haolanzheng/rebano.

Impact & The Road Ahead

The collective impact of this research is profound, pushing PINNs beyond theoretical exercises into practical, high-stakes applications. The advancements in efficiency and accuracy mean PINNs can now tackle problems previously deemed too computationally expensive or unstable, from turbulent fluid flows to complex quantum systems. The focus on robustness, uncertainty quantification, and interpretable physical constraints fosters greater trust in AI-driven scientific discovery and engineering design.

From enabling more precise non-invasive glucose monitoring (as seen in “Physics-Informed Neural Networks vs. Physics Models for Non-Invasive Glucose Monitoring: A Comparative Study Under Realistic Synthetic Conditions” by Riyaadh Gani from University College London) to developing real-time epidemic control strategies (“A Physics-Informed Neural Networks-Based Model Predictive Control Framework for SIR Epidemics” by Aiping Zhong et al. from South China University of Technology), PINNs are moving into critical societal domains. The integration with existing engineering tools, as shown by Moritz von Tresckow et al. (Technische Universität Darmstadt) in “Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains” for CAD geometries, bridges the gap between AI and traditional computational methods.

Looking ahead, the road for PINNs involves further integration of theoretical guarantees with practical implementation. Papers like “Non-Asymptotic Stability and Consistency Guarantees for Physics-Informed Neural Networks via Coercive Operator Analysis” by Ronald Katende from Kabale University provide crucial theoretical underpinnings, while innovations in adaptive sampling like RAMS (“RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations” by Weihang Ouyang et al. from Hong Kong Polytechnic University) and multi-objective optimization (as in “An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator Learning Network” by Binghang Lu et al. from Purdue University) promise even greater scalability and performance. The concept of digital twins, exemplified by P. Abbeel et al.’s work on “Towards Digital Twins for Optimal Radioembolization”, will continue to leverage PINNs for real-time simulation and optimization in fields like personalized medicine. The journey of PINNs is far from over, and these recent advancements mark an exciting chapter in bringing the power of physics-informed AI to solve the world’s most challenging problems.