16 citations · 41 across the 17 of their papers we have counts for
20 papers
Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions
Gabriel P. Langlois, Akwum Onwunta, Jérôme Darbon
Linear and convex quadratic programs are fundamental problems in optimization. While many methods have been developed for solving these programs in large-scale applications, to our…
S-PINN: Stochastic Separable Physics-Informed Neural Networks
Zhendong Li, Akwum Onwunta
Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for thi…
Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis
Amjad Seyedi, Lifang He, Songlin Zhao +2
Multimodal brain network analysis faces a persistent trade-off between predictive accuracy and interpretability. Deep neural networks achieve high accuracy but behave as black boxe…
Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations
Oluwatosin Akande, Gabriel P. Langlois, Akwum Onwunta
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization…
Stochastic Galerkin Method and Hierarchical Preconditioning for PDE-constrained Optimization
Zhendong Li, Akwum Onwunta, Bedřich Sousedík
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-op…
Quantum Differential Equation Solvers with Low State Preparation Cost: Eliminating the Time Dependence in Dissipative Equations
Gengzhi Yang, Akwum Onwunta, Dong An
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system…
Convex-concave splitting for the Allen-Cahn equation leads to -slow movement of interfaces
Patrick Dondl, Akwum Onwunta, Ludwig Striet +1
The convex-concave splitting discretization of the Allen-Cahn is easy to implement and guaranteed to be energy decreasing even for large time-steps. We analyze the time-stepping sc…
Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs
Oluwatosin Akande, Patrick Dondl, Kanan Gupta +2
We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine le…
Tensor train solution to uncertain optimization problems with shared sparsity penalty
Harbir Antil, Sergey Dolgov, Akwum Onwunta
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equ…
Fast-forwarding quantum algorithms for linear dissipative differential equations
Dong An, Akwum Onwunta, Gengzhi Yang
We establish improved complexity estimates of quantum algorithms for linear dissipative ordinary differential equations (ODEs) and show that the time dependence can be fast-forward…
Deep Nonnegative Matrix Factorization with Beta Divergences
Valentin Leplat, Le Thi Khanh Hien, Akwum Onwunta +1
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all exist…
Complexity analysis of regularization methods for implicitly constrained least squares
Akwum Onwunta, Clément W. Royer
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulat…
Smoothed Moreau-Yosida Tensor Train Approximation of State-constrained Optimization Problems under Uncertainty
Harbir Antil, Sergey Dolgov, Akwum Onwunta
We propose an algorithm to solve optimization problems constrained by partial (ordinary) differential equations under uncertainty, with almost sure constraints on the state variabl…
TTRISK: Tensor Train Decomposition Algorithm for Risk Averse Optimization
Harbir Antil, Sergey Dolgov, Akwum Onwunta
This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertain…
Optimal Control, Numerics, and Applications of Fractional PDEs
Harbir Antil, Thomas S. Brown, Ratna Khatri +3
This article provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several appli…
Novel Deep neural networks for solving Bayesian statistical inverse
Harbir Antil, Howard C Elman, Akwum Onwunta +1
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MC…
Reduced-order modeling for nonlinear Bayesian statistical inverse problems
Howard C. Elman, Akwum Onwunta
Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial d…
On the existence and uniqueness of the solution of a parabolic optimal control problem with uncertain inputs
Peter Benner, Akwum Onwunta, Martin Stoll
In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inp…
An inexact Newton-Krylov method for stochastic eigenvalue problems
Peter Benner, Akwum Onwunta, Martin Stoll
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product struct…
Solving optimal control problems governed by random Navier-Stokes equations using low-rank methods
Peter Benner, Sergey Dolgov, Akwum Onwunta +1
Many problems in computational science and engineering are simultaneously characterized by the following challenging issues: uncertainty, nonlinearity, nonstationarity and high dim…