Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

Fast and simple fluid simulator in Julia

Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia

A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.

Implementation of the Deep Q-learning algorithm to solve MDPs

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

Global glacier model using Universal Differential Equations for climate-glacier interactions

Atomic graph models for molecules and crystals in Julia

Nonlinear optical pulse propagator

FMIFlux.jl is a free-to-use software library for the Julia programming language, which offers the ability to place FMUs (fmi-standard.org) everywhere inside of your ML topologies and still keep the resulting model trainable with a standard (or custom) FluxML training process.

The automatically differentiable and GPU-compatible toolkit for CMB analysis.

An interface for accelerated simulation of high-dimensional collisionless and electrostatic plasmas.

Apply meaningful keys and custom behavior to indices.

Implementations of Infinitesimal Continuous Normalizing Flows Algorithms in Julia

An array type for MPI halo data exchange in Julia

General Relativistic Orbital Dynamics in Julia

MeshGraphNets.jl is a software package for the Julia programming language that provides an implementation of the MeshGraphNets framework by Google DeepMind for simulating mesh-based physical systems via graph neural networks.

From Semiconductor to TransistorLevel Modeling in Julia

Core methods and structures for neuroscience research in Julia.

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Propagate waves efficiently, optically, physically, differentiably with Julia Lang.

Train and sample Restricted Boltzmann machines in Julia

Julia package with several functions to train and analyze Autoencoder-based neural networks

A high-performance library for gradient based quantum optimal control

Convert output files generated with Trixi.jl to VTK.

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Optimal experimental design of ODE and DAE systems in julia

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Provides an array type designed for efficient appending and ease of use.

Unfortunately, FMUs (fmi-standard.org) are not differentiable by design. To enable their full potential inside Julia, FMISensitivity.jl makes FMUs fully differentiable, regarding to: states and derivatives | inputs, outputs and other observable variables | parameters | event indicators | explicit time | state change sensitivity by event

Package for fitting models according to the deep compartment modeling framework for pharmacometric applications.

Subspace Inference package for uncertainty analysis in deep neural networks and neural ordinary differential equations using Julia

A powerful, no code solution for control and systems engineering