Learning preconditioners for conjugate gradient PDE solvers

Y Li, PY Chen, T Du, W Matusik - … Conference on Machine …, 2023 - proceedings.mlr.press
Efficient numerical solvers for partial differential equations empower science and
engineering. One commonly employed numerical solver is the preconditioned conjugate …

Mmgp: a mesh morphing gaussian process-based machine learning method for regression of physical problems under nonparametrized geometrical variability

F Casenave, B Staber… - Advances in Neural …, 2023 - proceedings.neurips.cc
When learning simulations for modeling physical phenomena in industrial designs,
geometrical variabilities are of prime interest. While classical regression techniques prove …

Neural non-rigid tracking

A Bozic, P Palafox, M Zollhöfer, A Dai… - Advances in …, 2020 - proceedings.neurips.cc
We introduce a novel, end-to-end learnable, differentiable non-rigid tracker that enables
state-of-the-art non-rigid reconstruction by a learned robust optimization. Given two input …

Adaptive precision block-Jacobi for high performance preconditioning in the Ginkgo linear algebra software

G Flegar, H Anzt, T Cojean… - ACM Transactions on …, 2021 - dl.acm.org
The use of mixed precision in numerical algorithms is a promising strategy for accelerating
scientific applications. In particular, the adoption of specialized hardware and data formats …

Neural incomplete factorization: learning preconditioners for the conjugate gradient method

P Häusner, O Öktem, J Sjölund - arxiv preprint arxiv:2305.16368, 2023 - arxiv.org
Finding suitable preconditioners to accelerate iterative solution methods, such as the
conjugate gradient method, is an active area of research. In this paper, we develop a …

A deep conjugate direction method for iteratively solving linear systems

A Kaneda, O Akar, J Chen, VAT Kala… - International …, 2023 - proceedings.mlr.press
We present a novel deep learning approach to approximate the solution of large, sparse,
symmetric, positive-definite linear systems of equations. Motivated by the conjugate …

On the geometry transferability of the hybrid iterative numerical solver for differential equations

A Kahana, E Zhang, S Goswami, G Karniadakis… - Computational …, 2023 - Springer
The discovery of fast numerical solvers prompted a clear and rapid shift towards iterative
techniques in many applications, especially in computational mechanics, due to the …

Sustainable computational mechanics assisted by deep learning

A Oishi, G Yagawa - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
This paper proposes a method to promote power saving in the computational mechanics
simulations by deep learning. The method is expected to contribute to the achievement of …

Performance Study of Convolutional Neural Network Architectures for 3D Incompressible Flow Simulations

E Ajuria Illarramendi, M Bauerheim, N Ashton… - Proceedings of the …, 2023 - dl.acm.org
Recently, correctly handling spatial information from multiple scales has proven to be
essential in Machine Learning (ML) applications on Computational Fluid Dynamics (CFD) …

Neural Acceleration of Graph Based Utility Functions for Sparse Matrices

JD Booth, GS Bolet - IEEE Access, 2023 - ieeexplore.ieee.org
Many graph-based algorithms in high performance computing (HPC) use approximate
solutions due to having algorithms that are computationally expensive or serial in nature …