48 citations · 252 across the 96 of their papers we have counts for
11 papers · 1 filter
Data Assimilation with Deep Neural Nets Informed by Nudging
Harbir Antil, Rainald Löhner, Randy Price
The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly…
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…
A unified framework for optimal control of fractional in time subdiffusive semilinear PDEs
Harbir Antil, Ciprian G. Gal, Mahamadi Warma
We consider optimal control of fractional in time (subdiffusive, i.e., for ) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifyin…
Deep Neural Nets with Fixed Bias Configuration
Harbir Antil, Thomas S. Brown, Rainald Löhner +2
For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `…
Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions
Harbir Antil, Shodai Kubota, Ken Shirakawa +1
In this paper, we consider a class of optimal control problems governed by state-equations of Kobayashi--Warren--Carter type. The control is given by physical temperature. The focu…
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…
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
Harbir Antil, Rafael Arndt, Carlos N. Rautenberg +1
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint i…
Approximation of fractional harmonic maps
Harbir Antil, Sören Bartels, Armin Schikorra
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness…
Convergence Analysis of the Rank-Restricted Soft SVD Algorithm
Mahendra Panagoda, Tyrus Berry, Harbir Antil
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impract…
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Thomas S. Brown, Harbir Antil, Rainald Löhner +2
Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the num…
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…