Physics-Informed Neural Networks: Unlocking Robustness, Uncertainty, and Efficiency in Scientific AI

Latest 18 papers on physics-informed neural networks: Jan. 10, 2026

Physics-Informed Neural Networks (PINNs) have rapidly emerged as a powerful paradigm, marrying the data-driven capabilities of deep learning with the foundational principles of physics. This synergy promises to revolutionize scientific computing by tackling complex problems that traditional numerical methods often struggle with, from highly noisy data to intricate boundary conditions and uncertainty quantification. Recent research highlights a surge in innovation, pushing the boundaries of what PINNs can achieve, making them more robust, interpretable, and computationally efficient.

The Big Idea(s) & Core Innovations

One of the most pressing challenges in applying AI to real-world physical systems is dealing with imperfect data. Pietro de Oliveira Esteves from the Federal University of Ceará, in their paper “Robust Physics Discovery from Highly Corrupted Data: A PINN Framework Applied to the Nonlinear Schrödinger Equation”, introduces a robust PINN framework that acts as an effective physics-based filter. This innovation allows for the recovery of physical parameters from highly noisy data with remarkable accuracy (less than 0.2% error), showcasing PINNs’ potential in inverse problems where data is sparse or corrupted.

Further enhancing reliability, the ability to quantify uncertainty is paramount in critical applications. The paper “Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics” by Ibai Ramirez et al. from Mondragon University introduces a Bayesian PINN (B-PINN) that disentangles epistemic (model) and aleatoric (data) uncertainty. This provides more reliable and interpretable probabilistic predictions, crucial for prognostic health management in scenarios like transformer insulation aging. Similarly, “Physics-Informed Machine Learning for Transformer Condition Monitoring – Part II: Physics-Informed Neural Networks and Uncertainty Quantification” by J. I. Aizpurua et al. reinforces the importance of uncertainty quantification in predictive maintenance, building on robust PINN integrations.

Boundary conditions and complex geometries are perennial challenges. N. Sukumar and Ritwick Roy, from the University of California and 3DS Simulia, tackle this in “A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks”. Their novel Wachspress-based transfinite formulation ensures exact enforcement of Dirichlet boundary conditions on convex polygonal domains, improving accuracy and stability by guaranteeing a bounded Laplacian for the trial function. This approach generalizes Coons interpolation, opening doors for more complex geometries.

For more specialized and complex physical systems, new architectures and methodologies are emerging. “Müntz-Szász Networks: Neural Architectures with Learnable Power-Law Bases” by Gnankan Landry Regis N’guessan introduces MSNs, which learn fractional power exponents, significantly outperforming standard MLPs for functions with singular or fractional power behavior common in physics. Furthermore, “DBAW-PIKAN: Dynamic Balance Adaptive Weight Kolmogorov-Arnold Neural Network for Solving Partial Differential Equations” by Guokan Chen and Yao Xiao innovates by replacing traditional MLPs with Kolmogorov-Arnold Networks (KANs) and introducing a dynamic adaptive weighting strategy to mitigate spectral bias and enhance accuracy in solving PDEs. These architectural improvements address fundamental limitations of earlier PINN designs.

Beyond accuracy, efficiency and robustness are being actively addressed. Shivani Sainia et al. from NIT Hamirpur present A-PINN in “A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam”, an enhanced framework that uses auxiliary variables and balanced adaptive optimizers to achieve up to 40% better performance in structural vibration analysis. In fluid dynamics, Xuehui Qian et al. from Washington University in St. Louis propose a multi-stage PINN (MS-PINN) framework in “Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks” to solve nonlinear subsonic compressible flow in infinite domains. This approach uses coordinate transformations and asymptotic constraints to reach machine precision solutions, overcoming limitations of domain truncation.

Crucially, inverse problems are seeing transformative advances. Zihan Lin and QiZhi He from the University of Minnesota introduce LD-DIM in “Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Heterogeneous Subsurface Parameter Fields”, combining latent diffusion models with numerical solvers for robust subsurface parameter field reconstruction. This method leverages physics-constrained generative priors to handle ill-posedness, preserving sharp geological discontinuities better than PINNs and VAEs. Additionally, Shuwei Zhou et al. from RWTH Aachen University present KMINN in “Transfer-learned Kolosov-Muskhelishvili Informed Neural Networks for Fracture Mechanics”, integrating Williams enrichment with transfer learning for fracture mechanics, achieving sub-1% error in stress intensity factor evaluation and reducing computation time by over 70%.

Theoretical underpinnings are also being strengthened. “Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains” by Hao Zhang et al. from USTC provides rigorous theoretical guarantees for PINN convergence in fractional diffusion equations. “Spectral Analysis of Hard-Constraint PINNs: The Spatial Modulation Mechanism of Boundary Functions” by Yuchen XIE et al. unveils how boundary functions modulate the neural tangent kernel, providing crucial insights for principled PINN design. For broader generalizability, Chiuph et al. from Tsinghua University explore “Evolutionary Optimization of Physics-Informed Neural Networks: Advancing Generalizability by the Baldwin Effect”, demonstrating improved adaptability to new problems with reduced computational time.

Under the Hood: Models, Datasets, & Benchmarks

The innovations highlighted above are often powered by specific model architectures, advanced optimization strategies, and robust datasets:

• PINNs (Physics-Informed Neural Networks): The core model across most papers, continually refined with new components. For example, A-PINN introduces auxiliary loss functions and balanced adaptive optimizers, while DBAW-PIKAN incorporates the KAN architecture.
• Bayesian PINNs (B-PINNs): Utilized by Ibai Ramirez et al. for uncertainty quantification, incorporating heteroscedastic modeling to separate epistemic and aleatoric uncertainties.
• Müntz-Szász Networks (MSNs): A novel architecture from Gnankan Landry Regis N’guessan that replaces fixed activation functions with learnable power-law bases, demonstrating superior performance for singular functions.
• KMINN (Kolosov-Muskhelishvili Informed Neural Network): Developed by Shuwei Zhou et al. for fracture mechanics, integrates Williams enrichment and transfer learning.
• Multi-Stage PINNs (MS-PINN): Introduced by Xuehui Qian et al. to solve nonlinear subsonic compressible flow equations in infinite domains by iteratively minimizing residuals and incorporating asymptotic constraints.
• LD-DIM (Latent Diffusion for Differentiable Inverse Modeling): Proposed by Zihan Lin and QiZhi He, this framework combines latent diffusion models with numerical solvers for subsurface parameter field reconstruction.
• MAD-NG (Meta-Auto-Decoder Neural Galerkin Method): Developed by Qiuqi Li et al. enhances the Neural Galerkin Method for parametric PDEs through meta-learning and randomized sparse updates.
• Real-world Data: Applications like transformer insulation aging (e.g., Ibai Ramirez et al.) validate models against finite-element modeling and field measurements.
• Public Code Repositories: Researchers are committed to open science, with several papers providing code:
  • Robust Physics Discovery from Highly Corrupted Data
  • Evolutionary Optimization of Physics-Informed Neural Networks
  • Müntz-Szász Networks
  • Deep Learning in Geotechnical Engineering

However, it’s also worth noting some critical assessments, such as Krishna Kumar’s work from UC Berkeley, “Deep Learning in Geotechnical Engineering: A Critical Assessment of PINNs and Operator Learning”. This paper highlights that PINNs can be significantly slower and less accurate than traditional solvers in specific geotechnical applications, emphasizing the need for careful consideration of their applicability and highlighting the strength of automatic differentiation through traditional solvers for inverse problems.

Impact & The Road Ahead

The collective advancements in PINNs paint a picture of an increasingly powerful and versatile tool for scientific discovery and engineering. We’re moving towards PINNs that are not only more accurate but also more robust to noisy data, capable of quantifying their own uncertainty, and adept at handling complex geometries and multi-scale phenomena. The ability to integrate advanced neural architectures like KANs and MSNs, coupled with sophisticated training strategies and theoretical insights into convergence, marks a significant leap forward.

These breakthroughs promise to democratize high-fidelity simulations, accelerate inverse problem solving, and provide more reliable predictive models in fields ranging from material science and fluid dynamics to structural engineering and climate modeling. The open-sourcing of code also fosters rapid iteration and collaborative progress within the community.

Yet, challenges remain. The comparative analysis by Svetlana Roudenko et al. in “Soliton profiles: Classical Numerical Schemes vs. Neural Network-Based Solvers” shows that classical numerical methods still hold an edge in accuracy for certain 1D problems, and the critiques from Krishna Kumar remind us that PINNs are not a panacea. Future work will undoubtedly focus on pushing scalability to higher dimensions, enhancing computational efficiency further, and developing more sophisticated hybrid approaches that combine the best of both traditional numerical methods and deep learning. The road ahead for PINNs is exciting, promising to unlock new frontiers in physics-informed AI and scientific computing.