Scientific Machine Learning: Interpretable Neural Networks That Accurately Extrapolate From Small Data
January 14 2020 in Differential Equations, Julia, Mathematics, Science, Scientific ML | Tags: neural ode, physics-informed, sciml, small data, universal differential equations | Author: Christopher Rackauckas
The fundamental problems of classical machine learning are:
- Machine learning models require big data to train
- Machine learning models cannot extrapolate out of the their training data well
- Machine learning models are not interpretable
However, in our recent paper, we have shown that this does not have to be the case. In Universal Differential Equations for Scientific Machine Learning, we start by showing the following figure:
Indeed, it shows that by only seeing the tiny first part of the time series, we can automatically learn the equations in such a manner that it predicts the time series will be cyclic in the future, in a way … 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