Generalized Physics-Informed Learning through Language-Wide Differentiable Programming (Video)
March 31 2020 in Differential Equations, Mathematics, Science, Scientific ML | Tags: physics-informed machine learning, pinn, scientific machine learning, scientific ml, sciml | Author: Christopher Rackauckas
Chris Rackauckas (MIT), “Generalized Physics-Informed Learning through Language-Wide Differentiable Programming”
Scientific computing is increasingly incorporating the advancements in machine learning to allow for data-driven physics-informed modeling approaches. However, re-targeting existing scientific computing workloads to machine learning frameworks is both costly and limiting, as scientific simulations tend to use the full feature set of a general purpose programming language. In this manuscript we develop an infrastructure for incorporating deep learning into existing scientific computing code through Differentiable Programming (∂P). We describe a ∂P system that is able to take gradients of full Julia programs, making Automatic Differentiation a first class language feature and compatibility with deep learning pervasive. Our system utilizes the one-language nature of Julia package development to augment the existing package ecosystem with deep learning, supporting almost all language … READ MORE
Universal Differential Equations for Scientific Machine Learning (Video)
March 6 2020 in Uncategorized | Tags: neural ODEs, neural ordinary differential equations, scientific machine learning, scientific ml, sciml | Author: Christopher Rackauckas
Colloquium with Chris Rackauckas
Department of Mathematics
Massachusetts Institute of Technology
“Universal Differential Equations for Scientific Machine Learning”
Feb 19, 2020, 3:30 p.m., 499 DSL
https://arxiv.org/abs/2001.04385
Abstract:
In the context of science, the well-known adage “a picture is worth a thousand words” might well be “a model is worth a thousand datasets.” Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A … READ MORE
The Essential Tools of Scientific Machine Learning (Scientific ML)
August 20 2019 in Differential Equations, Julia, Mathematics, Programming, Scientific ML | Tags: ai, differential equations, natural language processing, scientific machine learning, scientific ml, sciml | Author: Christopher Rackauckas
Scientific machine learning is a burgeoning discipline which blends scientific computing and machine learning. Traditionally, scientific computing focuses on large-scale mechanistic models, usually differential equations, that are derived from scientific laws that simplified and explained phenomena. On the other hand, machine learning focuses on developing non-mechanistic data-driven models which require minimal knowledge and prior assumptions. The two sides have their pros and cons: differential equation models are great at extrapolating, the terms are explainable, and they can be fit with small data and few parameters. Machine learning models on the other hand require “big data” and lots of parameters but are not biased by the scientists ability to correctly identify valid laws and assumptions.
However, the recent trend has been to merge the two disciplines, allowing explainable models that are data-driven, require less data than traditional machine learning, and utilize the … READ MORE