Modeling and Simulation Group Meeting
A Festival of Machine Learning in Science at NYU (Part 2)
Speaker: Ben Peherstorfer, Laure Zanna, Eric Vanden-Eijnden, and Michael Lindsey
Location: TBA
Date: Thursday, April 8, 2021, 12:30 p.m.
Synopsis:
A series of short talks on recent applications of machine learning by a collection of speakers from chemistry, physics, and math.
Part II:
1. Benjamin Peherstorfer
"Modeling nonlinear low-dimensional dynamics with deep networks"
Deriving low-dimensional numerical models (model reduction) of partial
differential equations is challenging if the low-dimensional latent
dynamics are dominated by nonlinear behavior and thus linear
approximations in classical low-dimensional approximation spaces are
inefficient. Problems describing wave-type phenomena, strong
convection, and phase transitions with sharp gradients typically lead
to such latent dynamics. We parametrize low-dimensional latent models
via deep networks and show that exponentially faster error decays can
be achieved than with classical linear approximations. We discuss a
numerical time integration scheme for the proposed nonlinear latent
models and outline challenges and open problems.
2. Laure Zanna
“Rethinking ocean and climate physics with machine learning”
Climate change predictions remain uncertain in part due to the many small-scale turbulent processes, such as clouds or ocean mixing, that cannot be resolved. We will introduce two different machine learning techniques, equation-discovery and convolutional neural networks, to learn ocean turbulent processes that need to be represented in climate models. We will show that data-driven approaches can improve simulations but also potentially help us discover new physics.
3. Eric Vanden-Eijnden
"Promises and Challenges of Machine Learning in Scientific Computing"
The recent success of machine learning suggests that neural networks may be capable of approximating high-dimensional functions with controllably small errors. As a result, they could outperform standard function interpolation methods that have been the workhorses of current numerical methods.This feat offers exciting prospects for scientific computing, as it may allow us to solve problems in high-dimension once thought intractable. At the same time, looking at tools of machine learning through the lens of applied mathematics and numerical analysis can give new insights as to why and when neural networks can beat the curse of dimensionality. I will briefly discuss these issues, and present some applications related to solving PDE in large dimension and sampling high-dimensional probability distributions.
4. Michael Lindsey
"Optimization for variational Monte Carlo with neural quantum states"
We provide a high-level overview of variational Monte Carlo (VMC) for quantum many-body problems, where neural networks have recently been making an impact, and present some recent progress on both ground-state and excited-state optimization in VMC with neural quantum states.