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22.03 Release

Getting Started

  • Installation
    • System Requirements
    • Modulus with Docker Image (Recommended)
      • Install the Docker Engine
      • Install Modulus
        • Using the Modulus examples
    • Modulus Bare Metal Install
      • Using the Modulus examples
  • Release Notes
    • New features/Highlights v22.03
      • New Network Architectures
      • Modeling Enhancements
      • Training features
    • Feature Summary
    • Known Issues
  • Table of Contents
    • Example Index
      • Physics-Informed Foundations
      • Neural Operators
      • Intermediate Case Studies
      • Advanced Case Studies

Learn the Basics

  • Lid Driven Cavity Background
    • Problem Description
    • Case Setup
  • Creating Nodes
    • Importing the required packages
    • Creating a PDE Node
    • Creating a Neural Network Node
    • Using Hydra to Configure Modulus
  • Creating Geometry
  • Adding Constraints
    • Setting up the Domain
    • Boundary Constraints
    • PDE Constraints
    • Adding Validation Node
  • Training
    • Training the model
  • Results and Post Processing
    • Setting up Tensorboard
    • Output Files
  • Extra: Adding Monitor and Inferencer
    • Monitor Node
    • Inferencer Node

Theory

  • Physics-Informed Learning
    • Basic methodology
    • Monte-Carlo integration for loss formulation
    • Integral Equations
    • Parameterized Geometries
    • Inverse Problems
    • Weak solution of PDEs using PINNs
      • Classical solution, Strong solution, Weak solution
      • PINNs for obtaining weak solution
  • Architectures
    • Fourier Network
    • Modified Fourier Network
    • Highway Fourier Network
    • Multi-scale Fourier Feature Network
    • Spatial-temporal Fourier Feature Network
    • Sinusoidal Representation Networks (SiReNs)
    • DGM Architecture
    • Multiplicative Filter Network
    • Fourier Neural Operator
    • Adaptive Fourier Neural Operator
    • Physics Informed Neural Operator
    • Deep-O Net
    • Pix2Pix Net
    • Super Resolution Net
  • Advanced Schemes
    • Adaptive Activation Functions
    • Sobolev (Gradient Enhanced) Training
    • Importance Sampling
    • Quasi-Random Sampling
    • Exact Boundary Condition Imposition
    • Learning Rate Annealing
    • Homoscedastic Task Uncertainty for Loss Weighting
    • SoftAdapt
    • Relative Loss Balancing with Random Lookback (ReLoBRaLo)
    • GradNorm
    • Neural Tangent Kernel (NTK)
  • Recommended Practices
    • Physics Informed Neural Networks
      • Scaling the Problem
      • Integral Continuity Planes
      • Spatial Weighting of Losses (SDF weighting)
      • Increasing the Point Cloud Density
      • Gradient Aggregation
      • Exact Continuity
      • Symmetry
    • Operator Learning Networks
      • DeepONet
  • Miscellaneous Concepts
    • Generalized Polynomial Chaos
    • Relative Function Spaces and Integral Identities
      • \(L^p\) space
      • \(C^k\) space
      • \(W^{k,p}\) space
    • Integral Identities
    • Derivation of Variational Form Example

Modulus Features

  • Configuration
    • Minimal Example
    • Config Structure
    • Configuration Groups
      • Global Parameters
      • Architecture
        • Examples
      • Training
        • Parameters
      • Loss
      • Optimizer
      • Scheduler
    • Command Line Interface
    • Common Practices
      • Results Frequency
      • Changing Activation Functions
      • Multiple Architectures
      • Run Modes
  • Post Processing
    • TensorBoard in Modulus
      • Introduction
      • Workflow Overview
      • Lid Driven Cavity Example
    • VTK Utilities in Modulus
      • Introduction
      • Converting Variables to VTK Files
        • var_to_polyvtk
        • grid_to_vtk
      • VTK Validator and Inferencer
        • Constructing VTK Objects from Scratch
        • Reading VTK Objects from File
      • Voxel Inferencer
  • Parallel Training
    • Introduction
    • Running jobs using TF32 math mode
    • Running jobs using Just-In-Time (JIT) compilation
    • Running jobs using multiple GPUs

Physics-Informed Foundations

  • 1D Wave Equation
    • Introduction
    • Problem Description
    • Writing custom PDEs and boundary/initial conditions
    • Case Setup
      • Importing the required packages
      • Creating Nodes and Domain
      • Creating Geometry and Adding Constraints
      • Adding Validation data from analytical solutions
    • Results
    • Temporal loss weighting and time-marching schedule
  • 2D Wave Equation
    • Introduction
    • Problem Description
    • Problem Setup
    • Defining Boundary Conditions
    • Variable Velocity Model
    • Creating PDE and Neural Network Nodes
    • Creating Geometry
    • Adding Constraints
    • Validation
    • Results
  • Spring Mass ODE
    • Introduction
    • Problem Description
    • Case Setup
      • Defining the Equations
      • Solving the ODEs: Creating Geometry, defining ICs and making the Neural Network Solver
    • Results and Post-processing
  • Zero Equation Turbulence
    • Introduction
    • Problem Description
    • Case Setup
      • Importing the required packages
      • Defining the Equations, Networks and Nodes
      • Setting up domain, adding constraints and running the solver
  • Scalar Transport
    • Introduction
    • Problem Description
    • Case Setup
      • Importing the required packages
      • Creating Geometry
      • Defining the Equations, Networks and Nodes
      • Setting up the Domain and adding Constraints
      • Adding Monitors and Validators
    • Training the model
    • Results and Post-processing
  • Linear Elasticity
    • Introduction
    • Linear Elasticity in the Differential Form
      • Linear elasticity equations in the displacement form
      • Linear elasticity equations in the mixed form
      • Non-dimensionalized linear elasticity equations
      • Plane stress equations
      • Problem 1: Deflection of a bracket
        • Case Setup and Results
      • Problem 2: Stress analysis for aircraft fuselage panel
        • Case Setup and Results
    • Linear Elasticity in the Variational Form
      • Linear elasticity equations in the variational form
      • Problem 3: Plane displacement
        • Case Setup and Results
  • Inverse Problem
    • Introduction
    • Problem Description
    • Case Setup
      • Importing the required packages
      • Defining the Equations, Networks and Nodes for a Inverse problem
      • Assimilating data from CSV files/point clouds to create Training data
      • Adding Monitors
    • Training the model
    • Results and Post-processing

Neural Operators

  • Fourier
    • Introduction
    • Problem Description
    • Case Setup
      • Configuration
      • Loading Data
      • Initializing the Model
      • Adding Data Constraints
      • Adding Data Validator
    • Training the Model
      • Results and Post-processing
  • Adaptive Fourier
    • Introduction
    • Problem Description
    • Case Setup
      • Configuration
      • Loading Data
      • Initializing the Model
      • Adding Data Constraints and Validators
    • Training the Model
      • Results and Post-processing
  • Physics-Informed
    • Introduction
    • Problem Description
    • Case setup
      • Configuration
      • Defining PDE Loss
      • Loading Data
      • Initializing the Model
      • Adding Constraints
    • Training the Model
      • Results and Post-processing
      • Comparison to FNO
  • Deep-O Nets
    • Introduction
    • Problem Description
    • Problem 1: Data informed DeepONet
      • Date Preparation
      • Case Setup
    • Problem 2: Physics informed DeepONet
      • Case Setup

Intermediate Case Studies

  • Variational Examples
    • Introduction
    • Problem Description
    • Variational Form
    • Continuous type formulation
      • Creating the Geometry
      • Defining the Boundary conditions and Equations to solve
      • Creating the Validator
      • Creating the Inferencer
      • Creating and the Solver
      • Creating the Variational Loss
      • Results and Post-processing
    • Point source and Dirac Delta function
      • Creating the Geometry
      • Creating the Variational Loss and Solver
      • Results and Post-processing
  • Geometry from STL Files
    • Introduction
    • Problem Description
    • Case Setup
      • Importing the required packages
      • Using STL files to generate point clouds
      • Defining the Equations, Networks and Nodes
      • Setting up Domain and adding Constraints
      • Adding Validators and Monitors
    • Training the model
    • Results and Post-processing
    • Accelerating the Training of Neural Network Solvers via Transfer Learning
  • Time Window Training
    • Introduction
    • Problem Description
    • Case Setup
      • Sequence of Train Domains
      • Sequence Solver
    • Results and Post-processing
  • Electromagnetics
    • Introduction
    • Problem 1: 2D Waveguide Cavity
      • Case Setup
      • Results
    • Problem 2: 2D Dielectric slab waveguide
      • Case setup
      • Results
    • Problem 3: 3D waveguide cavity
      • Problem setup
      • Case setup
      • Results
    • Problem 4: 3D Dielectric slab waveguide
      • Case setup
      • Results
  • 2D Turbulent Channel
    • Introduction
    • Problem Description
    • Governing Equations
      • Standard Wall Functions
      • Launder Spalding Wall Functions
    • Case Setup - Standard Wall Functions
      • Custom Aggregator
    • Case Setup - Launder Spalding Wall Functions
    • Post-processing, Results and Discussion
  • Turbulence Super Resolution
    • Introduction
    • Problem Description
    • Writing a Custom Data-Driven Constraint
    • Writing a Custom Data-Driven Validator
    • Case Setup
      • Configuration
      • Loading Data
      • Initializing the Model
      • Adding Data Constraints
      • Adding Data Validator
    • Training the Model
      • Results and Post-processing

Advanced Case Studies

  • Conjugate Heat Transfer
    • Introduction
    • Problem Description
    • Case Setup
      • Creating Geometry
      • Neural network, Nodes and Multi-Phase training
      • Setting up Flow Domain and Constraints
        • Inlet, Outlet and Channel and Heat Sink walls
        • Interior
        • Integral Continuity
      • Setting up Thermal Multi-Phase Domain and Constraints
        • Inlet, Outlet and Channel walls:
        • Fluid and Solid Interior:
        • Fluid-Solid Interface:
        • Heat Source:
      • Adding Validators and Monitors
    • Training the Model
    • Results and Post-processing
      • Plotting gradient quantities: Wall Velocity Gradients
  • 3D Fin Parameterization
    • Introduction
    • Problem Description
    • Case Setup
      • Creating Nodes and Architecture for Parameterized Problems
      • Setting up Domain and Constraints
    • Training the Model
    • Design Optimization
    • Results
  • Heat Transfer with High Conductivity
    • Introduction
    • 2D Solid-Solid Heat Transfer
    • 2D Solid-Fluid Heat Transfer
  • FPGA
    • Introduction
    • Problem Description
    • Case Setup
    • Solver using Fourier Network Architecture
    • Leveraging Symmetry of the Problem
    • Imposing Exact Continuity
    • Results, Comparisons, and Summary
  • Industrial Heat Sink
    • Introduction
    • Problem Description
    • Case Setup
      • Defining Domain
      • Sequence Solver
    • Results and Post-processing
    • gPC-Based Surrogate Modeling Accelerated via Transfer Learning

Modulus API

  • Core API
    • modulus
      • modulus.aggregator
      • modulus.arch
      • modulus.constants
      • modulus.constraint
      • modulus.derivatives
      • modulus.graph
      • modulus.key
      • modulus.loss
      • modulus.node
      • modulus.pdes
      • modulus.trainer
    • modulus.architecture
      • architecture.afno
      • architecture.deeponet
      • architecture.dgm
      • architecture.fno
      • modulus.architecture.fourier_net
      • architecture.fully_connected
      • architecture.hash_encoding_net
      • architecture.highway_fourier_net
      • architecture.modified_fourier_net
      • architecture.moving_time_window
      • architecture.multiplicative_filter_net
      • architecture.multiscale_fourier_net
      • architecture.pix2pix
      • architecture.radial_basis
      • architecture.siren
      • architecture.super_res_net
    • modulus.continuous
      • continuous.constraints.constraint
      • continuous.dataset.dataset
      • continuous.domain.domain
      • continuous.inferencer.inferencer
      • continuous.monitor.monitor
      • continuous.solvers.solver
      • continuous.validator.validator
    • modulus.discrete
      • discrete.constraints.constraint
      • discrete.dataset.datafile
      • discrete.dataset.dataset
      • discrete.solvers.solver
      • discrete.validator.validator
    • modulus.hydra
      • hydra.arch
      • hydra.config
      • hydra.hydra
      • hydra.loss
      • hydra.optimizer
      • hydra.profiler
      • hydra.scheduler
      • hydra.training
      • hydra.utils
    • modulus.geometry
      • geometry.geometry
      • geometry.csg.adf
      • geometry.csg.csg
      • geometry.csg.csg_1d
      • geometry.csg.csg_2d
      • geometry.csg.csg_3d
      • geometry.csg.curves
      • geometry.tessellation.tessellation
    • modulus.PDES
      • PDES.advection_diffusion
      • PDES.basic
      • PDES.diffusion
      • PDES.electromagnetic
      • PDES.energy_equation
      • PDES.linear_elasticity
      • PDES.navier_stokes
      • PDES.signed_distance_function
      • PDES.turbulence_zero_eq
      • modulus.PDES.wave_equation
  • Post Processing API
    • modulus.csv_utils
      • csv_utils.csv_rw
    • modulus.plot_utils
      • plot_utils.vtk
    • modulus.tensorboard_utils
      • tensorboard_utils.plotter
  • Utilities
    • modulus.sympy_utils
      • sympy_utils.functions
      • sympy_utils.numpy_printer
      • sympy_utils.torch_printer
    • modulus.vpinn_utils
      • vpinn_utils.integral
      • vpinn_utils.test_functions
Modulus
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Welcome to the Modulus API documentation.

Core API¶

  • modulus
  • modulus.architecture
  • modulus.continuous
  • modulus.discrete
  • modulus.hydra
  • modulus.geometry
  • modulus.PDES

Post Processing API¶

  • modulus.csv_utils
  • modulus.plot_utils
  • modulus.tensorboard_utils

Utilities¶

  • modulus.sympy_utils
  • modulus.vpinn_utils
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