Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems
Aleksandra JekicAfroditi NatsaridouSigne Riemer-S{\o}rensenHelge LangsethOdd Erik Gundersen
Aug 2026
Machine Learning
Abstract
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for which many properties and limitations remain unknown.
PINNs are widely accepted as less computationally efficient and accurate than traditional methods for solving PDEs, such as the finite element method. However, PINNs are commonly claimed to show promise in solving inverse problems and handling noisy or incomplete data. We compare the performance of PINNs in solving inverse problems with that of a traditional approach using the finite element method combined with a numerical optimizer. The models are tested on viscosity identification in 1D Burgers' equation and in 2D/3D Taylor-Green Vortex, in all cases with additive Gaussian noise applied to training and validation data.
We find that while PINNs may require less human effort and specialized knowledge, they are outperformed by the traditional approach. For example, for 2D Taylor-Green Vortex with {\sigma}=1 noise, the baseline has a mean prediction RMSE of 0.0013 compared to 0.01 for the best PINN variation. However, PINNs scale better than the baseline with the computational complexity of the problem. We identify failures during training to be addressed if the PINN performance on noisy inverse problems is to become more competitive.
This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-physics FFF simulation results into a deep neural network (DNN), thus ensuring consistency with physical laws: (1) incorporate physics constraints within the loss function of the DNN, (2) use physics model outputs as additional inputs to the DNN model, and (3) pre-train a DNN model with physics model input-output and then update it with experimental data. These strategies help to enforce a physically consistent relationship between bond quality and tensile strength, thus making porosity predictions physically meaningful. Eight different combinations of the above strategies are investigated. The results show how the combination of multiple strategies produces accurate machine learning models even with limited experimental data.
B. Kapusuzoglu, S. Mahadevan· JOM· 79 citations· ⚡2
This work introduces a pioneering exploration of Self-Supervised Learning (SSL) within the SNN, and proposes a novel Spiking Self-Attention (SSA) and Spiking Transformer (Spikformer) that achieves 80+% accuracy on ImageNet.
Zhaokun Zhou, Kaiwei Che, Wei Fang et al.· arXiv.org· 69 citations· ⚡10
This paper considers global sensitivity analysis (GSA) for situations where both a physics-based model and experimental observations are available, and investigates physics-informed machine learning strategies to effectively combine the two sources of information in order to maximize the accuracy of the sensitivity estimate.
B. Kapusuzoglu, S. Mahadevan· Reliability Engineering & Sy...· 45 citations
EquiPocket is proposed, an E(3)-equivariant Graph Neural Network for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms.
Yang Zhang, Wenbing Huang, Zhewei Wei et al.· International Conference on...· 43 citations· ⚡4
An adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs is developed that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model.
B. Kapusuzoglu, S. Mahadevan, Shunsaku Matsumoto et al.· Structural And Multidiscipli...· 17 citations
An improved variant of nearest neighbors (NN) for estimation with missing data in latent factor models that provides a (near-)quadratic improvement in the non-asymptotic error and admits a significantly narrower asymptotic confidence interval when compared to both unit-unit or time-time NN.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
