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Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

The topology optimization of artificial neural networks can be particularly difficult if the fitness evaluations require expensive experiments or simulations. For that reason, the optimization methods may need to be supported by surrogate…

Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty…

Neural networks (NNs) lack measures of "reliability" estimation that would enable reasoning over their predictions. Despite the vital importance, especially in areas of human well-being and health, state-of-the-art uncertainty estimation…

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…

Artificial Neural Networks (NNWs) are appealing functions to substitute high dimensional and non-linear history-dependent problems in computational mechanics since they offer the possibility to drastically reduce the computational time.…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…

Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…

We study the feasibility of data based machine learning applied to ultrasound tomography to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in…

Accurate modeling of fluid dynamics around complex geometries is critical for applications such as aerodynamic optimization and biomedical device design. While advancements in numerical methods and high-performance computing have improved…

Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…

This study develops and validates neural network frameworks with physics-based constraints for surrogate modeling of rarefied gas dynamics across different levels of complexity. As a baseline, we first examine the BGK kinetic relaxation…

The Hessian of a neural network captures parameter interactions through second-order derivatives of the loss. It is a fundamental object of study, closely tied to various problems in deep learning, including model design, optimization, and…

Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality…

In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy.…

Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…