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The criticality problem in nuclear engineering asks for the principal eigenpair of a Boltzmann operator describing neutron transport in a reactor core. Being able to reliably design, and control such reactors requires assessing these…
Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…
The Iterative Quasi-Monte Carlo method, or iQMC, replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for more accurate and efficient solutions to the neutron transport equation.…
The clinical management of several cardiovascular conditions, such as pulmonary hypertension, require the assessment of the right ventricular (RV) function. This work addresses the fully automatic and robust access to one of the key RV…
In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct…
Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we…
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and we use recurrent neural…
Detection and classification of pulmonary nodules is a challenge in medical image analysis due to the variety of shapes and sizes of nodules and their high concealment. Despite the success of traditional deep learning methods in image…
High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical…
As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank…
This paper presents a study of the effectiveness of Neural Network (NN) techniques for deconvolution inverse problems relevant for applications in Quantum Field Theory, but also in more general contexts. We consider NN's asymptotic limits,…
In this work, we address two major issues in recent Denoising Diffusion Probabilistic Models (DDPM): {\bf 1)} geometric key feature extraction and {\bf 2)} network equivariance. Since the DDPM prediction network relies on the U-net…
Training recurrent neural networks (RNNs) to perform neuroscience-style tasks has become a popular way to generate hypotheses for how neural circuits in the brain might perform computations. Recent work has demonstrated that task-trained…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
Deep Reinforcement Learning has enabled the learning of policies for complex tasks in partially observable environments, without explicitly learning the underlying model of the tasks. While such model-free methods achieve considerable…
In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…
Due to their flexibility and predictive performance, machine-learning based regression methods have become an important tool for predictive modeling and forecasting. However, most methods focus on estimating the conditional mean or specific…
We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of partial differential equations (PDEs). Our primary concern is…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…