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 and Large Projects using SciML

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

• DJ4Earth: Differentaible Programming / SciML for Climate Modeling

• QuantumOptics

• New York Federal Reserve Bank

• Julia Robotics

• Julia Computing: JuliaSim

• Pumas-AI: Pharmaceutical Modeling and Simulation

  • SciML and Pumas-AI tools are an accepted standard by the FDA with trained evaluators

• Brazilian National Institute for Space Research (INPE)

  • Julia and the satellite Amazonia-1

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

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

• ModiaSim: Modia.jl

• Safe Blues: A Method for Estimation and Control in the Fight Against COVID-19

• InSysBio: Heta Project QSP Simulation

• Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia

Press Coverage Featuring SciML

• Using machine learning to derive black hole motion from gravitational waves (using SciML DiffEqFlux)

• HPCWire: Argonne AI for Science Colloquium Marks Challenges and Progress

• Pumas-AI looks to democratize access to drug development tools (using SciML)

• 13 NumFOCUS Projects Awarded CZI Grants

• List23: The Open Source HetaSimulator project is going to be launched by InSysBio

• PR Newswire: InSysBio to launch its OpenSource HetaSimulator project

• Wall Street Journal: Why Artificial Intelligence Isn’t Intelligent (Julia Computing CEO Viral Shah Quoted Discussing SciML applications)

• Williams Welcomes Julia Computing as Dorilton Ventures Partner (Formula 1 Racecar Team Partners to use SciML)

• NREL Open-Source Modeling Approach Cracks the Code of Simulating Low-Inertia Power Systems (uses SciML)

• Julia Computing Raises $24M Series A, Former Snowflake CEO Bob Muglia Joins Board (products built using SciML)

• Julia Computing Launches JuliaSim for Scientific ML In Cloud

• Julia Computing Launches JuliaSim For Scientific Machine Learning In Cloud

• Julia Computing introduces JuliaSim, next-generation cloud-based simulation platform

• United Therapeutics uses SciML for CFD/PDEs

• SafeBlues Release (3/16/2021) (analysis done with SciML)

  • Gizmodo: Researchers Are Working on a Virtual Phone Virus That 'Mimics' the Spread of Covid-19

  • El Universal: Covid-19. Crean virus virtual que se propaga por Bluetooth en tu móvil

  • DailyMail: A virtual Bluetooth virus spread between SMARTPHONES 'could help us track Covid-19 more accurately', study claims

  • QS Noticias: Crearon un virus que infecta smartphones cercanos para probar cómo funciona el distanciamiento social

  • MarseilleNews.net: Ce virus virtuel transmettant Bluetooth peut imiter la propagation du COVID

  • MIT CCE News: Researchers develop Bluetooth powered “virtual virus” to track COVID-19’s spread

  • la100 Cienradios: Crearon un “virus digital” que podría rastrear el coronavirus

  • Mobile Bulgaria: Виртуален вирус пресъздава моделите на разпространение на COVID-19

  • LaMinute.info: Le virus du téléphone virtuel « imite » la propagation de Covid-19

  • Manlokam: ఇదొక స్పెషల్‌ వైరస్.. బ్లూటూత్ ద్వారా పనిచేస్తూ కోవిడ్‌ను గుర్తిస్తుంది..

  • ambitio: Propagan un virus virtual que imita al coronavirus

  • El Pais: DESARROLLAN UN VIRUS PARA MÓVILES QUE SE PROPAGA COMO SI FUERA LA COVID-19

  • La Repubblica: Il virus 'virtuale' mima Covid e sa dire come viaggia l'epidemia

  • Amarujala.com: ब्लूटूथ से फोन में फैलता है यह खास वायरस, कोरोना ट्रैक करने में करता है मदद

  • pplware: “Vírus virtual” transmite-se entre smartphones ao estilo do coronavírus

  • Spider's Web: Naukowcy chcą stworzyć cyfrowego koronawirusa. Pomoże w monitorowaniu tego biologicznego

  • LokMat News 18: ब्लूट्यूथने फोनमध्ये पसरतो हा खास व्हायरस; Coronavirus ट्रॅक करण्यासाठी होते मदत

  • Ajel News: فيروس افتراضي ينتقل بالبلوتوث يساعد في تتبع انتشار «كورونا»

  • 4gnews: Investigadores criam "coronavirus digital" transmissível aos smartphones por Bluetooth

  • Upvarta News: ब्लूटूथ से मोबाइल में दस्तक देगा ये खास Virus , जानें क्या है वर्चुअल वायरस

  • Youm7: تطوير فيروس افتراضى ينتشر عبر البلوتوث بين الهواتف الذكية لتتبع كورونا

  • El Universal: Covid-19. Crean virus virtual que se propaga por Bluetooth en tu móvil

  • MobileSyrup: Researchers develop virtual mobile virus to better understand COVID-19 spread

  • 20 Minutos: 'Safe Blues', el nuevo virus virtual que se contagia entre móviles imitando al coronavirus

  • LaFM: Aparece virus que infecta smartphones de manera 'similar' al coronavirus

  • DeobreProgramy: Safe Blues: wirus na smartfony ma pomóc w badaniu COVID-19

  • Playtech.ro: Virusul pentru telefon care „imită” răspândirea COVID-19. Ce e Safe Blues și cum funcționează

  • Pingvin.pro: Віртуальний вірус для смартфонів допоможе оцінити поширення COVID-19

  • SecurityLab.ru: Передающийся по Bluetooth вирус поможет в оценке распространения COVID-19

  • Explica.co: ‘Safe Blues’, the new virtual virus that spreads between mobiles imitating the coronavirus

  • juventudrebelde.cu: Desarrollan virus de teléfonos móviles que se replica por cercanía, como el SARSCov-2

  • The Next Web: Scientists want to unleash a Bluetooth-powered ‘virtual virus’ to study COVID-19

  • Pinakait: A ‘safe’ virus that transfers via Bluetooth created to predict Covid-like virus spread

  • WoahTech: Bluetooth Transmitting ‘Safe’ Virus Developed To Track COVID Spread

  • News 21: A ‘safe’ virus that transfers via Bluetooth created to predict Covid-like virus spread

  • 24-e News: They create a laboratory cell phone virus that simulates the spread of COVID-19

  • JioForMe: Designed a secure “virtual” epidemic .Spreading it will help us learn about COVID

  • Prowell Tech: This Bluetooth-transmitting virtual virus can mimic COVID spread

  • Olhar Digital: Researchers create “virtual virus” to study the spread of Covid-19

  • MobyGeek: Researchers Developed Virtual Phone Virus To Recreate How COVID-19 Spreads

  • Tech Codex: Researchers develop virtual mobile virus to better understand COVID-19 spread

  • The Canadian: Researchers Develop Virtual Mobile Viruses to Better Understand the Spread of COVID-19

  • Technology Fortnight: A ‘safe’ virus that transfers via Bluetooth created to predict Covid-like virus spread

  • Times of India: A ‘safe’ virus that transfers via Bluetooth created to predict Covid-like virus spread

  • Flipboard UK: Virtual virus that transmits between phones developed to mimic COVID spread

  • ZDNet: Researchers develop Bluetooth-transmitting 'virus' to improve COVID-19 tracking accuracy

  • GadgetsNow: A ‘safe’ virus that transfers via Bluetooth created to predict Covid-like virus spread

  • guncelkal: Researchers Are Working on a Virtual Phone Virus That ‘Mimics’ the Spread of Covid-19

  • Newsbreak: Researchers Are Working on a Virtual Phone Virus That 'Mimics' the Spread of Covid-19

  • Android Authority: Virtual virus that transmits between phones developed to mimic COVID spread

  • The Conversation: We’ve designed a safe ‘virtual’ epidemic. Spreading it is going to help us learn about COVID (using SciML)

• Analytics India Magazine: Julia Computing Receives Funding To Accelerate Electronics Simulation Using AI & ML (using SciML)

• HPC Wire: Julia Computing Receives DARPA Award to Accelerate Electronics Simulation by 1,000x (with SciML tools)

• Apostolato Digitale: Intelligenza Artificiale in parrocchia (Video)

• Synced Review: The Best AI Technology Developed in the Past 3 to 5 Years: “Scientific Machine Learning” (2020 in Review With Viral B. Shah)

• entwickler.de: „Julia ist bei einfachen Machine-Learning-Aufgaben mit Python vergleichbar, aber besser geeignet für komplexere.“

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

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

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

• JaxEnter: Julia: The programming language of the future? (SciML mentioned as a popular tool)

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

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

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

• HPCWire: What’s New in Computing vs. COVID-19: Julia, Twitter, TACC & More

• InsideBigData: Pumas-AI Launches Julia Language-Based Software to Advance Drug Development, Patient Care (powered by SciML)

• JaxEnter: “Julia is comparable to Python for simple machine learning tasks and better for complex ones”

• ArsTechnica: The unreasonable effectiveness of the Julia programming language (discussion on DifferentialEquations.jl)

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

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

• Analytics India Magazine: How Julia Computing Just Gave A Push To High-Performance GPU Computing (SciML for GPUs mentioned)

• Technical.ly: JuliaCon is the stage for a week of programming talks — and a new Baltimore company (Pumas-AI, Powered by SciML)

• NewsWise: University of Maryland, Baltimore Researchers' Startup, Pumas-AI, Launches Cutting-Edge Healthcare Software (Pumas-AI, 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

• The Age: 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

• Fundamentals of Numerical Computation

• 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

Awards Associated with SciML Software

• 2021: International Society of Pharmacology (ISoP) Mathematics and Computing Special Interest Group Poster Award. Niklas Korsbo (Pumas-AI, University of Cambridge), Chris Elrod (Julia Computing), Francesco Brizzi (Roche), Antoine Soubret (Roche), Andreas Noack (Julia Computing), Vijay Ivaturi (Pumas-AI, University of Maryland School of Pharmacy) and Christopher Rackauckas (Julia Computing, MIT): For "Automatic identification of non-obvious prognostic factors in big data with DeepNLME". DeepNLME is built using the SciML tooling.

• 2021: United States Department of the Air Force Artificial Intelligence Accelerator Scientific Excellence Award (Chris Rackauckas): For "For developing innovative computational processes to accelerate the simulation of nonlinear systems using neural networks".

• 2021: Mediterranean Machine Learning School Outstanding Poster Award (Simone Azeglio, Valerio Pagliarino, Francesco Calisto, Luca Bottero, Martina S., Sara Tiengo, Giovanni Graziano): For "Physics-Informed Machine Learning Simulator for Wildfire Propagation" with NeuralPDE.jl.

• 2020: International Society of Pharmacology (ISoP) Emerging Scientist Award (Chris Rackauckas): For development of SciML and Pumas.

• 2020: American Conference on Pharmacometrics (ACoP) Quality Award (Chris Rackauckas and Vijay Ivaturi): For DiffEqGPU accelerating QSP models by 175x.

• 2020: IEEE High-Performance Extreme Computing (HPEC) Outstanding Paper Award (Chris Rackauckas and Qing Nie): For the high-performance adaptive SDE solvers in StochasticDiffEq.jl.

• 2019: International Society of Pharmacology (ISoP) Mathematics and Computing Special Interest Group Poster Award (Chris Rackauckas and Vijay Ivaturi): Koopman operator tooling of DiffEqUncertainty.jl accelerating uncertainty quantification in PK/PD modeling by 100x.

• 2018 Julia Community Award (Chris Rackauckas): For development of SciML (at the time, named JuliaDiffEq).

• DSWeb 2018 Dynamical Systems Software Contest: Runner up is DifferentialEquations.jl and a winner is DynamicalSystems.jl which utilizes DifferentialEquations.jl.

• 2017: Best Speaker Award, Tsukuba Global Science Week (Chris Rackauckas): Presentation on StochasticDiffEq.jl for systems biology.

Podcasts and Developer Interviews

• Notamonadtutorial.com: Modeling complexity with Symbolics.jl and ModelingToolkit.jl (Interview with Chris Rackauckas)

• Jousef Murad: Chris Rackauckas - Physics-Informed Neural Networks (PINNs) | Podcast #42

• The Stardust Podcast #7 - Christopher Rackauckas

• JuliaLang AMA: Ask us anything, SciML edition: Chris Rackauckas and Yingbo Ma

• ACEMS Podcast, Episode 25: Safe Blues

• Notamonadtutorial.com: Scientific Machine Learning with Julia: the SciML ecosystem (Interview with Chris Rackauckas)

External Blog Posts and Presentations

• Integro Differential Equations GSoC 2021 NumFOCUS: Final Report

• Spatial SSAs GSOC 2021 Final Report

• StructuralIdentifiability.jl Google Summer of Code: Final Results

• Discretizations of Partial Differential Equations: GSoC'21 : Final Report

• Sensitivity Analysis of Hybrid Differential Equations

• Tutorial on using spatial SSAs in DiffEqJump

• Neural Hybrid Differential Equations and Adjoint Sensitivity Analysis

• Shadowing Methods for Forward and Adjoint Sensitivity Analysis of Chaotic Systems

• Neural Hybrid Differential Equations

• Bayesian Inference using Julia and TuringLang at Stuttgart Julia Programming

• First achievements: Next Subvolume Method

• hustf's blog: Ordinary differential equations (ODE)

• Adam Davis: DiffEqFlux — Differential Equations and Neural Networks

• StochasticLifestyle: ModelingToolkit, Modelica, and Modia: The Composable Modeling Future in Julia

• StochasticLifestyle: Generalizing Automatic Differentiation to Automatic Sparsity, Uncertainty, Stability, and Parallelism

• Adam MacLean: A thread on teaching dynamical systems in Julia

• Jesse Perla: Machine Learning and High Dimensional Economics

• Experiments with Neural ODEs in Julia

• StochasticLifestyle: JuliaCall Update: Automated Julia Installation for R Packages

• 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

• StochasticLifestyle: 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

• Faster Policy Learning with Continuous-Time Gradients

• 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