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Learning Oscillatory Navier-Stokes Flows and Causal Linear Operators with Deep Neural Network Algorithms

SIAM News – 

Lizuo Liu delivered a minisymposium presentation on this research at the 2022 SIAM Conference on Mathematics of Data Science (MDS22), which took place in San Diego, Ca., last year. He received funding to attend MDS22 through a SIAM Student Travel Award. 

Learning Oscillatory Navier-Stokes Flows and Causal Linear Operators with Deep Neural Network Algorithms

By Lizuo Liu and Wei Cai

Much of the lively research activity in machine learning (ML) for scientific computing stems from the power of deep neural networks (DNNs), which are known for their expressibility and effective handling of high-dimensional data. ML has revolutionized tasks such as natural language processing, image and speech recognition, and recommender systems, while scientific computing contributes to the solution of many complex mathematical and physical problems in areas like physics, chemistry, biology, and engineering.

By combining ML and scientific computing, researchers and engineers can leverage ML’s strengths to tackle challenging problems that were previously unsolvable. ML techniques can help analyze large amounts of high-dimensional data from simulations and experiments in scientific computing, thus providing insights that would otherwise be difficult to obtain. On the other hand, researchers can use scientific computing to design and optimize complex ML models, ultimately yielding more accurate and efficient algorithms.

ML’s introduction into scientific computing has already led to breakthroughs in various fields, including drug discovery, climate modeling, and materials science. As ML and scientific computing continue to advance, the opportunities for further integration and cross-fertilization will be boundless.

Here, we will explore the utilization of ML techniques in the realm of computational mathematics. The first project that we will describe uses neural networks (NNs) to address nonlinear problems with highly oscillatory solutions, while the second project employs NNs to approximate operators that represent causal physical systems. READ THE FULL ARTICLE