SciML Scientific Machine Learning Showcase

The purpose of this page is to demonstrate the various applications where the SciML tools have been employed. If you would like your own work added to this list, please open a pull request.

External Applications Libraries

There are many external libraries which connect and utilize SciML utilities under the hood. The following an incomplete list of software organizations providing domain modeling tools that are built upon SciML. If you would like your institution's tools added to the list, please open a pull request.

• CliMA: Climate Modeling Alliance

• QuantumOptics

• New York Federal Reserve Bank

• Julia Robotics

• Pumas-AI: Pharmaceutical Modeling and Simulation

• Brazilian National Institute for Space Research (INPE)

• CMU+MIT+Citrine: Accelerated Computational Electrochemical Systems Discovery (ACED)

• Los Alamos National Lab: Model Analysis & Decision Support (MADS)

• ModiaSim: Modia.jl

Press Releases Featuring SciML

• New MIT (SciML) Model Could Help Determine Quarantine Measures Needed to Reduce COVID-19’s Spread

• Slowing the spread of Covid-19 (with SciML models)

• TWiV 653: Back to school with COVID-19 (SciML used to develop school reopening strategies in Southern California for COVID-19)

• SciML Software (through Pumas) is utilized in an FDA-approved submission

• MIT-led team to develop (SciML) software to help forecast space storms

• The Air Force’s Latest GPS Alternative: Earth’s Magnetic Fields (research powered by SciML)

• The road to electric vehicles with lower sticker prices than gas cars – battery costs explained (research powered by SciML)

• Air Force Is Looking At Using Magnetic Fields To Navigate Instead Of GPS And Flight Testing It On F-16s (Algorithms Powered by SciML)

• Cornell Chronicle: Digital ‘virus’ helps researchers map potential spread

• Phys.org: Digital 'virus' helps researchers map potential spread

• latronet.gr: Χαρτογράφηση εξάπλωσης CoViD-19 με κινητό τηλέφωνο

• Popular Deep Learning Frameworks: An Overview (DiffEqFlux.jl mentioned)

• ZDNet: Could a neural network have predicted this pandemic’s impact?

• UQ News: A mathematical framework could help safely ease social distancing

• MIT News: Model quantifies the impact of quarantine measures on Covid-19’s spread

• TechXplore: Machine learning algorithm quantifies the impact of quarantine measures on COVID-19's spread

• COVID-19 simulator could help track virus spread as restrictions eased

• Pfizer uses Julia (SciML) to accelerate simulations of new therapies for metabolic diseases up to 175x

• The Brazilian National Institute for Space Research (INPE) plans space missions with SciML

• JaxEnter: Machine learning meets math: Solve differential equations with new Julia library

• Julia (SciML) is awarded funded through the ARPA-E DIFFERENTIATE Program

• The Federal Reserve Bank of New York publishes its trademark Dynamic Stochastic General Equilibrium models in Julia and utilizes SciML tooling

Books

• Statistics with Julia

• The Koopman Operator in Systems and Control

  • "All simulations have been performed in Julia, with additional Julia packages: LinearAlgebra.jl, Random.jl, Plots.jl, Lasso.jl, DifferentialEquations.jl"

Media

External Blog Posts and Presentations

• Experiments with Neural ODEs in Julia

• CFD tutorial in Julia

• Neural ODE for Reinforcement Learning and Nonlinear Optimal Control: Cartpole Problem Revisited

• "Modeling control of run-of-river power plant Grønvollfoss" in Julia

• Physics-informed neural networks (PINNs) solver on Julia

• Utkarsh's Blog: Performance Enhancements and Optimizations for Differential Equation solvers, GSoC Blog: Final Report

• GPU-Accelerated ODE Solving in R with Julia, the Language of Libraries

• Francesco Martinuzzi: Google Summer of Code 2020 Final Report

• High weak order solvers and adjoint sensitivity analysis for stochastic differential equations

• High weak order SDE solvers

• Francesco Martinuzzi: GSoC week 11: Gated Recurring Unit-based reservoir

• Francesco Martinuzzi: GSoC week 10: Reservoir Memory Machines

• Francesco Martinuzzi: GSoC week 9: Cycle Reservoirs with Regular Jumps

• Utkarsh's Blog: Second Evaluations (Parallel Extrapolation Methods)

• Neural ODEs as continuous network layers

• Physics-informed neural networks (PINNs) solver on Julia. GSoC 2020. Second evaluation.

• Ludovico: July deliverables: Two new surrogates methods and benchmarking

• Francesco Martinuzzi: GSoC week 7: Reservoir Computing with Cellular Automata Part 1

• Francesco Martinuzzi: GSoC week 6: minimum complexity echo state network

• Working with Differential Equations and Neural Networks

• Francesco Martinuzzi: Data-driven prediction of chaotic systems: comparison of Echo State Network variations

• Working with Differential Equations and Neural Networks

• Kirill Zubov: Physics-informed neural networks (PINNs) solvers on Julia

• Sebastian Callh personal blog: Forecasting the weather with neural ODEs

• Utkarsh's Blog: Community Bonding & First Evaluation (BDF & NDF methods)

• Ludovico: From JSOC to GSOC: a new beginning with Surrogates.jl

• Francesco Martinuzzi: GSoC week 4: SVD-based Reservoir

• Francesco Martinuzzi: GSoC week 3: Echo State Gaussian Processes

• SCIML: LOGICIELS LIBRES POUR L'APPRENTISSAGE MACHINE SCIENTIFIQUE

• Fitting the SIR model to Covid-19 fatality data

• Francesco Martinuzzi: GSoC week 2: Support Vector Regression in Echo State Networks

• Frank Schäfer: GSoC 2020: High weak order SDE solvers and their utility in neural SDEs

• Modeling pandemics subject to stochastic uncertainties – A polynomial chaos approach

• Francesco Martinuzzi: GSoC week 1: lasso, Elastic Net and Huber loss

• Utkarsh's Blog: GSoC 2020 with The Julia Language, Performance Enhancements and Optimisations for Differential Equation solvers

• awesome-ode-neural-networks

• Modelling and data analysis tools to study the 2020 COVID-19 outbreak

• awesomeJulia

• Kevin Hannay: Differential Equations as a Neural Network Layers

• Safe Blues — The Measurement Tool for Responsible Easing of Social Distancing

• Per-Olof Persson and Robert Sweeney Blanco: The DifferentialEquations Package

• Current status of neural differential equations and the importance of language

• Phylodynamics of SARS-CoV-2, Simon Frost (Microsoft Health Futures)

• Francesco Martinuzzi: A brief introduction to Reservoir Computing

• Nicolau Leal Werneck: Fitting the SIR model to Covid-19 fatality data

• SIR Model for COVID-19: Estimating R0, Roberto Berwa, MIT

• StochasticLifestyle: How To Train Interpretable Neural Networks That Accurately Extrapolate From Small Data

• Awesome Julia: A nice list of resources to start from

• Machine Learning aided Epidemiology: COVID-19 Global quarantine strength and reproduction number evolution

• StochasticLifestyle: How Inexact Models Can Guide Decision Making in Quantitative Systems Pharmacology

• JuliaLang: GSoC and JSoC 2020 Project List

• StochasticLifestyle: Recent advancements in differential equation solver software

• StochasticLifestyle: A Collection of Jacobian Sparsity Acceleration Tools for Julia

• Pankaj Mishra: A Summer with Jacobians

• JuliaLang: Hello @DiffEqBot

• Ludovico: New Surrogates and final plans

• Julia DifferentialEquations.jl to model an explosion load

• Ludovico: More optimization methods and future surrogates

• Ludovico: Surrogate optimization and Sampling

• Toby Driscoll: Matlab vs. Julia vs. Python

• Ludovico: New abstract types: RadialBasis and Kriging.

• Ludovico: Bonding-time, or should I say coding time?

• StochasticLifestyle: The Essential Tools of Scientific Machine Learning (Scientific ML)

• StochasticLifestyle: Neural Jump SDEs (Jump Diffusions) and Neural PDEs

• MIT Open Courseware: Modern Differential Equations Solver Software: Where We Are and Where We're Headed

• JuliaLang: DiffEqFlux.jl – Julia 的神經微分方程套件

• JuliaLang: DiffEqFlux.jl – A Julia Library for Neural Differential Equations

• FluxML: Differentiable Control Problems

• EpiRecipes: SIR model in Julia using DifferentialEquations

• Ronan Chagas: The Satellite Toolbox for Julia

• StochasticLifestyle: Some State of the Art Packages in Julia v1.0

• Julia, my new friend for computing and optimization?

• JuliaCon 2018: Solving PDEs in Julia

• Ronan Chagas: Changes in OrdinaryDiffEq v3

• Mathieu Besançon: Winter warm-up: toy models for heat exchangers

• Ronan Chagas: Extending the ODE Solutions in Julia by Creating Custom Data Arrays for the Simulations

• UCI Data Science Initiative: A Quick Tour of DifferentialEquations.jl

• StochasticLifestyle: Why Numba and Cython are not substitutes for Julia

• Ronan Chagas: Using julia to simulate systems composed of continuous and discrete parts

• StochasticLifestyle: Solving Systems of Stochastic PDEs and using GPUs in Julia

• JuliaLang: GSoC 2017 : A Wrapper for the FEniCS Finite Element Toolbox

• JuliaLang: GSoC 2017: Efficient Discretizations of PDE Operators

• JuliaLang: NeuralPDE.jl: A Neural Network solver for ODEs

• StochasticLifestyle: Some Fun With Julia Types: Symbolic Expressions in the ODE Solver

• JuliaLang: GSoC 2017: Native Julia second order ODE and BVP solvers

• Yiannis Simillides blog: FEniCS.jl: Second "Approximate" Month

• Yiannis Simillides blog: FEniCS.jl: First "Approximate" Month

• Mathieu Besançon: DifferentialEquations.jl - part 2: decision from the model

• Mathieu Besançon: Getting started with DifferentialEquations.jl

• StochasticLifestyle: A Comparison Between Differential Equation Solver Suites In MATLAB, R, Julia, Python, C, Mathematica, Maple, and Fortran