1 code implementation • 15 Mar 2024 • S. Chandra Mouli, Danielle C. Maddix, Shima Alizadeh, Gaurav Gupta, Andrew Stuart, Michael W. Mahoney, Yuyang Wang
Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers.
1 code implementation • 29 Dec 2023 • Jin-Long Wu, Matthew E. Levine, Tapio Schneider, Andrew Stuart
Complex dynamical systems are notoriously difficult to model because some degrees of freedom (e. g., small scales) may be computationally unresolvable or are incompletely understood, yet they are dynamically important.
no code implementations • 9 Feb 2023 • Tapio Helin, Andrew Stuart, Aretha Teckentrup, Konstantinos Zygalakis
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost of evaluating the data likelihood.
1 code implementation • 19 Aug 2021 • Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets.
2 code implementations • 13 Jun 2021 • Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping.
17 code implementations • ICLR 2021 • Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces.
4 code implementations • NeurIPS 2020 • Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks.
no code implementations • 13 May 2020 • Dmitry Burov, Dimitrios Giannakis, Krithika Manohar, Andrew Stuart
The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian.
6 code implementations • ICLR Workshop DeepDiffEq 2019 • Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces.
no code implementations • 31 Aug 2017 • Tapio Schneider, Shiwei Lan, Andrew Stuart, João Teixeira
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems.