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Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the…
We analyze a high order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection-diffusion equation posed in a domain with piecewise-wise $\mathcal{C}^2$ boundary $\partial \Omega$.…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs) which…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Partitioning transportation networks into balanced and spatially coherent traffic zones is a fundamental yet computationally challenging task in intelligent transportation systems. The resulting optimization problem exhibits dense…
We generalize the two-channel (Edwards) fermion-boson model describing quantum transport in a background medium to the more realistic case of dispersive bosons. Using the variational exact diagonalization technique, we numerically solve the…
Spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for Computational Fluid Dynamics (CFD). Mesh skewness is then typically encountered causing severe deterioration of…
We represent the method of dynamic diffusion for the approximate solution of Shroedinger equation with decoherence. Decoherence shows as the divergency of exact solution from the dynamics of diffusion swarm, which arises when the total…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…