Related papers: Trustworthy AI in numerics: On verification algori…

Validation accuracy is a necessary, but not sufficient, measure of a neural network classifier's quality. High validation accuracy during development does not guarantee that a model is free of serious flaws, such as vulnerability to…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…

Inference accuracy of deep neural networks (DNNs) is a crucial performance metric, but can vary greatly in practice subject to actual test datasets and is typically unknown due to the lack of ground truth labels. This has raised significant…

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be…

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential)…

Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into…

This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…

Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…

This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…

Many optimization problems of interest are known to be intractable, and while there are often heuristics that are known to work on typical instances, it is usually not easy to determine a posteriori whether the optimal solution was found.…

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often…

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks…

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in…