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Colloquium with Chris Rackauckas

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"Universal Differential Equations for Scientific Machine Learning" Colloquium with Chris Rackauckas Department of Mathematics Massachusetts Institute of Technology Feb 19, 2020 https://www.sc.fsu.edu/news-and-event...

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Colloquium with Chris Rackauckas

3Likes

300Views

2020Feb 21

Intro

0:00

Convolutional Neural Networks Are Structure Assumptions

1:27

Ecology Example: Lotka-Volterra Equations

2:46

Heterogeneous scientific data is encoded in the structure scientific models

4:13

Transcript

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Colloquium with Chris Rackauckas

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Intro

Intro

Intro

Convolutional Neural Networks Are Structure Assumptions

Convolutional Neural Networks Are Structure Assumptions

Convolutional Neural Networks Are Structure Assumptions

Ecology Example: Lotka-Volterra Equations

Ecology Example: Lotka-Volterra Equations

Ecology Example: Lotka-Volterra Equations

Heterogeneous scientific data is encoded in the structure scientific models

Heterogeneous scientific data is encoded in the structure scientific models

Heterogeneous scientific data is encoded in the structure scientific models

Mechanistic vs Non-Mechanistic Models

Mechanistic vs Non-Mechanistic Models

Mechanistic vs Non-Mechanistic Models

Pros and Cons of Mechanistic Models

Pros and Cons of Mechanistic Models

Pros and Cons of Mechanistic Models

Neural Networks = Nonlinear Function Approximation

Neural Networks = Nonlinear Function Approximation

Neural Networks = Nonlinear Function Approximation

Universal Differential Equations

Universal Differential Equations

Universal Differential Equations

License

Choices for families

Colloquium with Chris Rackauckas

Chapters

Intro

Intro

Intro

Convolutional Neural Networks Are Structure Assumptions

Convolutional Neural Networks Are Structure Assumptions

Convolutional Neural Networks Are Structure Assumptions

Ecology Example: Lotka-Volterra Equations

Ecology Example: Lotka-Volterra Equations

Ecology Example: Lotka-Volterra Equations

Heterogeneous scientific data is encoded in the structure scientific models

Heterogeneous scientific data is encoded in the structure scientific models

Heterogeneous scientific data is encoded in the structure scientific models

Mechanistic vs Non-Mechanistic Models

Mechanistic vs Non-Mechanistic Models

Mechanistic vs Non-Mechanistic Models

Pros and Cons of Mechanistic Models

Pros and Cons of Mechanistic Models

Pros and Cons of Mechanistic Models

Neural Networks = Nonlinear Function Approximation

Neural Networks = Nonlinear Function Approximation

Neural Networks = Nonlinear Function Approximation

Universal Differential Equations

Universal Differential Equations

Universal Differential Equations

Universal ODEs learn and extrapolate Lotka-Volterra from small data!

Universal ODEs learn and extrapolate Lotka-Volterra from small data!

Universal ODEs learn and extrapolate Lotka-Volterra from small data!

Discretized PDE Operators are Convolutions

Discretized PDE Operators are Convolutions

Discretized PDE Operators are Convolutions

Automatically Learning PDEs from Data: Universal PDEs for Fisher-KPP

Automatically Learning PDEs from Data: Universal PDEs for Fisher-KPP

Automatically Learning PDEs from Data: Universal PDEs for Fisher-KPP

Universal SDEs: Nonlinear Timeseries Learning and Extrapolation

Universal SDEs: Nonlinear Timeseries Learning and Extrapolation

Universal SDEs: Nonlinear Timeseries Learning and Extrapolation

Universal PDEs for Acceleration: Automated Climate Parameterizations

Universal PDEs for Acceleration: Automated Climate Parameterizations

Universal PDEs for Acceleration: Automated Climate Parameterizations

Universal ODES Accelerate Non- Newtonian Fluid Simulations

Universal ODES Accelerate Non- Newtonian Fluid Simulations

Universal ODES Accelerate Non- Newtonian Fluid Simulations

Neural Network Surrogates for Real-Time Nonlinear Approximate Control

Neural Network Surrogates for Real-Time Nonlinear Approximate Control

Neural Network Surrogates for Real-Time Nonlinear Approximate Control

A Complimentary Inversion Network

A Complimentary Inversion Network

A Complimentary Inversion Network

Inversion is accurate and independent of simulation time

Chapters

Chapters