Related papers: Energy-based error bound of physics-informed neura…
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…
We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates…
We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…
In energy intensive industrial systems, an evaporative cooling process may introduce operational flexibility. Such flexibility refers to a systems ability to deviate from its scheduled energy consumption. Identifying the flexibility, and…
We obtain a denoising loss bound of the recently proposed neural network based universal discrete denoiser, Neural DUDE, which can adaptively learn its parameters solely from the noise-corrupted data, by minimizing the \emph{empirical…
A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
The rapid growth of deep neural networks (DNNs) has brought increasing attention to their energy use during training and inference. Here, we establish the thermodynamic bounds on energy consumption in quasi-static analog DNNs by mapping…
In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…
Accurate prediction of vehicle collision dynamics is crucial for advanced safety systems and post-impact control applications, yet existing methods face inherent trade-offs among computational efficiency, prediction accuracy, and data…
Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged…
Accurate and interpretable bearing fault classification is critical for ensuring the reliability of rotating machinery, particularly under variable operating conditions where domain shifts can significantly degrade model performance. This…
We present a physics-informed neural network framework for predicting the mechanical performance of elastomers exposed to concurrent thermal and gamma-radiation exposure, such as elastomers in nuclear cables or space electronics. Our…
One use case of ``physics-informed neural networks'' (PINNs) is solution reconstruction, which aims to estimate the full-field state of a physical system from sparse measurements. Parameterized governing equations of the system are used in…
Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…
Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical…
We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by…
Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have…
Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…