NVIDIA Modulus: Physics ML 開発のためのフレームワーク
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Nvidia Modulus is a framework designed for developing physics-informed machine learning models, particularly for creating digital twins in various industrial applications. It utilizes simulation data and physics equations to build robust surrogate models that can generalize across different configurations and scenarios. Key use cases include modeling reacting flows in industrial boilers and addressing fluid accelerated corrosion in steam generators.
![Key Consepts
NVIDIA MODULUS
Framework for Developing Physics ML Models for Digital Twins
Use simulation and observation data and governing physics
equations to generate a robust surrogate model
Generalizes parameterized domain and physics to encapsulate
multiple configurations/scenarios in the trained model
Builds a Physics ML model/digital twin to iterate on the
design/operating space
Forward simulation, inverse and data assimilation problems
What its not? Not a Solver, Not a Simulation platform
GETTING STARTED WITH AI FOR ENGINEERING SIMULATIONS USING MODULUS ON
RESCALE PLATFORM [S42087]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-4-320.jpg)
![12
Physics-ML categorization
Physics
Data
Fully data
driven
Inductive
bias
Physics
constrained
Fully physics
driven
DEVELOPING DIGITAL TWINS FOR WEATHER, CLIMATE, AND ENERGY [S41823]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-5-320.jpg)
![NVIDIA MODULUS A FRAMEWORK
Key Concepts
Specify governing equations
Symbolic equations
Integral form or weak form
extensible
Loss function minimization
Satisfy the PDE
Boundary conditions
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-7-320.jpg)
![CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]
NVIDIA MODULUS A FRAMEWORK
Key Concepts
Specify governing equations
Symbolic equations
Integral form or weak form
extensible
Loss function minimization
Satisfy the PDE
Boundary conditions
Explicit Parameterization
S41823: Towards developing digital twins for weather, climate, and energy](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-8-320.jpg)
![DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]
Formulationand PINN vs CFD
PINN for reacting flows
7
Aim: Create a digital twin of an industrial scale boiler
Simplified methane oxidation
Implemented reacting flow transport equations for
kinetics-controlled combustion
No requirement for training data
Single PINN model for a range of input conditions
Fidelity and accuracy comparable to CFD
Trained PINN can provide near-instantaneous
inference for any input condition
Figure source: https://commons.wikimedia.org/wiki/File:Steam_Generator.png](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-17-320.jpg)
![Towards a reacting flow solver
8
Governing equations: Strongly coupled PDEs
Single species
Turbulent
Steady state
2D
Multiple species
Turbulent
Steady state
2D
Multiple species
Reacting
Turbulent
Steady state
2D
Multiple species
Reacting
Turbulent
Transient
2D
Multiple species
Reacting
Turbulent
Transient
3D
Continuity:
Species mass fraction: +
Momentum:
Temperature:
Kinetics-controlled single step irreversible reaction
Species source/sink terms etc
Temperature source term
DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-18-320.jpg)
![PINN vs CFD
Simplified systems
14
AnsysFluent Modulus AnsysFluent Modulus
REACTANT
PRODUCT
AnsysFluent Modulus
Species distributions for case without T source term Temperature distribution with frozen species
DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-19-320.jpg)
![DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]
Handling large T-source
Resolving the issue with large T-source
16
T-source dominates the Y-source
This can lead to imbalances between the backpropagated
gradients
B) Transient approach
Handles large source terms by
learning the change between
states instead of learning
everything at once
Uses a moving time window
approach
A) Gradient normalization approach
Attempts to remove the dominance
of any component of the global loss
function
Dynamically assigns weights to
different constraints](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-20-320.jpg)
![CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]
Unrestricted © Siemens Energy, 2021
7
August 2021
A typical Heat Recovery Steam Generator and some challenges
for Digitalization
Exhaust gas flow and temperatur
Low Pressor Evaporator
Mix of steam and liquid
changes with operations
Area of evaporation changes
with operations
Point of corrosion difficult to
predict
But
Thousands of pipes, no
sensors
Fluid dynamics depend on
geometry, only 2D drawings
available](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-22-320.jpg)
![Unrestricted © Siemens Energy, 2021
9
August 2021
The Fluid Accelerated Corrosion Workflow
Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions
Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh
generation (possible iterations)
Different operating conditions for creating
reduced order model response surface
Current
process
Better
process?
The challenge of the current approach:
Detailed simulation take months to prepare for one plant
Costs exceed customer benefits
Simplified data driven approaches do not determine the risk level in
an acceptable manner
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-23-320.jpg)
![HRSG WORKFLOW WITH MODULUS
Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions
Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh
generation (possible iterations)
Different operating conditions for creating
reduced order model response surface
Current process
New suggested
process
2D drawing Centerline
geometry
3D geometry
for Fluids
Using standard
CAD tools
< 0.5 hr
Convert 2D drawings to
centerline geometry
(~0.5 day)
Geometry : 2D 3D
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-24-320.jpg)
![HRSG WORKFLOW WITH MODULUS
Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions
Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh
generation (possible iterations)
Different operating conditions for creating
reduced order model response surface
Current process
Model Training
Mesh free, fast point cloud generation
Incompressible NS eqs
Fourier feature neural network
Parameterized input velocity
New suggested
process
2D drawing Centerline
geometry
3D geometry
for Fluids
Using standard
CAD tools
< 0.5 hr
Convert 2D drawings to
centerline geometry
(~0.5 day)
Geometry : 2D 3D
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-25-320.jpg)
![HRSG WORKFLOW WITH MODULUS
PySDF
module, Optix for Sampling and SDF
Defining network architecture
Symbolic definition of equations
Verification and
Validation
Fourier Feature Network
Hyperparameter tuning and training
A B C
Good match (in A,B,C):
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-26-320.jpg)
![HRSG WORKFLOW WITH MODULUS
Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions
Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh
generation (possible iterations)
Different operating conditions for creating
reduced order model response surface
Current process
Model Training Infer new scenario
Suggested
process
Order of 10,000x speed up per scenario
Order of seconds inference time vs 8 hr
per CFD run
2D drawing Centerline
geometry
3D geometry
for Fluids
Using standard
CAD tools
< 0.5 hr
Convert 2D drawings to
centerline geometry
(~0.5 day)
Geometry : 2D 3D
Mesh free, fast point cloud generation
Incompressible NS eqs
Fourier feature neural network
Parameterized input velocity
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-27-320.jpg)
![MODULUS OMNIVERSE INTEGRATION
Modulus Omniverse extension:
enables importing outputs of Modulus trained model into a visualization pipeline for common output scenarios ex:
streamlines, iso-surface
provides an interface that enables interactive exploration of design variables/parameters to infer new system behavior
Visualization Extension
Modulus Extension in Omniverse
Visualization
pipeline
Model Outputs Output Rendering
Interactive
exploration
Model inference
CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS
AND OMNIVERSE [S41671]](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-29-320.jpg)
![LERN MORE
GTC2022 sessions
§ Getting Started with AI for Engineering Simulations using Modulus on Rescale Platform [S42087]
§ Case Study on Developing Digital Twins for the Power Industry using Modulus and Omniverse [S41671]
§ Developing Digital Twins for Energy Applications using Modulus [S41325]
§ Developing Digital Twins for Weather, Climate, and Energy [S41823]
NVIDIA Modulus documentation
§ https://docs.nvidia.com/deeplearning/modulus/index.html
Blog
§ Siemens Energy Taps NVIDIA to Develop Industrial Digital Twin of Power Plant in Omniverse](https://image.slidesharecdn.com/naruhikotmodulus-220428064028/85/NVIDIA-Modulus-Physics-ML-31-320.jpg)
NVIDIA Modulus: Physics ML 開発のためのフレームワーク
- 1. NVIDIA MODULUS: PHYSICS-ML 開発のためのフレームワーク NARUHIKO TAN | HPC SOLUTION ARCHITECT
- 2. AGENDA What is NVIDIA Modulus? Use cases § Reacting flow in industrial scale boiler § Fluid accelerated corrosion of heat recovery steam generator
- 3. AGENDA What is NVIDIA Modulus? Use cases § Reacting flow in industrial scale boiler § Fluid accelerated corrosion of heat recovery steam generator
- 4. Key Consepts NVIDIA MODULUS Framework for Developing Physics ML Models for Digital Twins Use simulation and observation data and governing physics equations to generate a robust surrogate model Generalizes parameterized domain and physics to encapsulate multiple configurations/scenarios in the trained model Builds a Physics ML model/digital twin to iterate on the design/operating space Forward simulation, inverse and data assimilation problems What its not? Not a Solver, Not a Simulation platform GETTING STARTED WITH AI FOR ENGINEERING SIMULATIONS USING MODULUS ON RESCALE PLATFORM [S42087]
- 5. 12 Physics-ML categorization Physics Data Fully data driven Inductive bias Physics constrained Fully physics driven DEVELOPING DIGITAL TWINS FOR WEATHER, CLIMATE, AND ENERGY [S41823]
- 6. NVIDIA MODULUS – A FRAMEWORK Key Consepts Specifying geometry of the domain § STL or Constructive Solid Geometry (CSG) § Specify sampling policy § Specify parameterization Using ground truth data in Modulus § Observed data or simulation data § Use only the governing equations with no data § Use only data § Use both § Consistent with first principles § Faster convergence Network architectures – Curated networks § Fourier Features (FN), Sinusoidal Representation (SiReNs), Modified Fourier Features (mFN) § Fourier Neural Operator, Adaptive Fourier Neural Operator § Fully Connected (FC) § Deep Galerkin Method (DGM) § Modified Highway Networks § Multiplicative Filter Networks and more…
- 7. NVIDIA MODULUS A FRAMEWORK Key Concepts Specify governing equations Symbolic equations Integral form or weak form extensible Loss function minimization Satisfy the PDE Boundary conditions CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 8. CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671] NVIDIA MODULUS A FRAMEWORK Key Concepts Specify governing equations Symbolic equations Integral form or weak form extensible Loss function minimization Satisfy the PDE Boundary conditions Explicit Parameterization S41823: Towards developing digital twins for weather, climate, and energy
- 9. 15 MODULUS FRAMEWORK - VERIFICATION CFD Solid Mechanics Acoustics Laminar Turbulent MODULUS FRAMEWORK - VERIFICATION
- 10. 16 Electromagnetics Vibrations Turbulence MODULUS FRAMEWORK - VERIFICATION Modulus Modulus Modulus MODULUS FRAMEWORK - VERIFICATION
- 11. MODULUS FRAMEWORK - VERIFICATION Taylor-Green Vortex Decay
- 12. 12 A100 FP32 vs. TF32: Results, Compute Time, Loss MODULUS FRAMEWORK - PERFORMANCE SINGLE GPU: Tensor Core Speed-up for PDEs
- 13. 13 MODULUS FRAMEWORK - PERFORMANCE MULTI-GPU/NODE Scalability
- 14. 14 AI IN SCIENCE & ENGINEERING Improved Physics & Predictions AI IN SCIENCE & ENGINEERING
- 15. AGENDA What is NVIDIA Modulus? Use cases § Reacting flow in industrial scale boiler § Fluid accelerated corrosion of heat recovery steam generator
- 16. 16 USE CASES § REACTING FLOW IN INDUSTRIAL SCALE BOILER
- 17. DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325] Formulationand PINN vs CFD PINN for reacting flows 7 Aim: Create a digital twin of an industrial scale boiler Simplified methane oxidation Implemented reacting flow transport equations for kinetics-controlled combustion No requirement for training data Single PINN model for a range of input conditions Fidelity and accuracy comparable to CFD Trained PINN can provide near-instantaneous inference for any input condition Figure source: https://commons.wikimedia.org/wiki/File:Steam_Generator.png
- 18. Towards a reacting flow solver 8 Governing equations: Strongly coupled PDEs Single species Turbulent Steady state 2D Multiple species Turbulent Steady state 2D Multiple species Reacting Turbulent Steady state 2D Multiple species Reacting Turbulent Transient 2D Multiple species Reacting Turbulent Transient 3D Continuity: Species mass fraction: + Momentum: Temperature: Kinetics-controlled single step irreversible reaction Species source/sink terms etc Temperature source term DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]
- 19. PINN vs CFD Simplified systems 14 AnsysFluent Modulus AnsysFluent Modulus REACTANT PRODUCT AnsysFluent Modulus Species distributions for case without T source term Temperature distribution with frozen species DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325]
- 20. DEVELOPING DIGITAL TWINS FOR ENERGY APPLICATIONS USING MODULUS [S41325] Handling large T-source Resolving the issue with large T-source 16 T-source dominates the Y-source This can lead to imbalances between the backpropagated gradients B) Transient approach Handles large source terms by learning the change between states instead of learning everything at once Uses a moving time window approach A) Gradient normalization approach Attempts to remove the dominance of any component of the global loss function Dynamically assigns weights to different constraints
- 21. USE CASES § FLUID ACCELERATED CORROSION OF HEAT RECOVERY STEAM GENERATOR
- 22. CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671] Unrestricted © Siemens Energy, 2021 7 August 2021 A typical Heat Recovery Steam Generator and some challenges for Digitalization Exhaust gas flow and temperatur Low Pressor Evaporator Mix of steam and liquid changes with operations Area of evaporation changes with operations Point of corrosion difficult to predict But Thousands of pipes, no sensors Fluid dynamics depend on geometry, only 2D drawings available
- 23. Unrestricted © Siemens Energy, 2021 9 August 2021 The Fluid Accelerated Corrosion Workflow Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh generation (possible iterations) Different operating conditions for creating reduced order model response surface Current process Better process? The challenge of the current approach: Detailed simulation take months to prepare for one plant Costs exceed customer benefits Simplified data driven approaches do not determine the risk level in an acceptable manner CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 24. HRSG WORKFLOW WITH MODULUS Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh generation (possible iterations) Different operating conditions for creating reduced order model response surface Current process New suggested process 2D drawing Centerline geometry 3D geometry for Fluids Using standard CAD tools < 0.5 hr Convert 2D drawings to centerline geometry (~0.5 day) Geometry : 2D 3D CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 25. HRSG WORKFLOW WITH MODULUS Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh generation (possible iterations) Different operating conditions for creating reduced order model response surface Current process Model Training Mesh free, fast point cloud generation Incompressible NS eqs Fourier feature neural network Parameterized input velocity New suggested process 2D drawing Centerline geometry 3D geometry for Fluids Using standard CAD tools < 0.5 hr Convert 2D drawings to centerline geometry (~0.5 day) Geometry : 2D 3D CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 26. HRSG WORKFLOW WITH MODULUS PySDF module, Optix for Sampling and SDF Defining network architecture Symbolic definition of equations Verification and Validation Fourier Feature Network Hyperparameter tuning and training A B C Good match (in A,B,C): CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 27. HRSG WORKFLOW WITH MODULUS Geometry : 2D 3D CFD Model preparation 3D CFD operating conditions Full 3D geometry from 2D drawing Geometry preparation for CFD, mesh generation (possible iterations) Different operating conditions for creating reduced order model response surface Current process Model Training Infer new scenario Suggested process Order of 10,000x speed up per scenario Order of seconds inference time vs 8 hr per CFD run 2D drawing Centerline geometry 3D geometry for Fluids Using standard CAD tools < 0.5 hr Convert 2D drawings to centerline geometry (~0.5 day) Geometry : 2D 3D Mesh free, fast point cloud generation Incompressible NS eqs Fourier feature neural network Parameterized input velocity CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 28. Materials Physics AI Path-Tracing USD NVIDIA OMNIVERSE ENTERPRISE Platform for Creating and Connecting Virtual Worlds Designer, Creator, Engineer Collaborators NVIDIA Core Technology RTX Renderer Nucleus Portal
- 29. MODULUS OMNIVERSE INTEGRATION Modulus Omniverse extension: enables importing outputs of Modulus trained model into a visualization pipeline for common output scenarios ex: streamlines, iso-surface provides an interface that enables interactive exploration of design variables/parameters to infer new system behavior Visualization Extension Modulus Extension in Omniverse Visualization pipeline Model Outputs Output Rendering Interactive exploration Model inference CASE STUDY ON DEVELOPING DIGITAL TWINS FOR THE POWER INDUSTRY USING MODULUS AND OMNIVERSE [S41671]
- 30. NEW FEATURES IN MODULUS V22.03 § New network architectures § Fourie Neural Operator § Physics Informed Neural Operator § Adaptive Fourier Neural Operator § Deep-O Net § Modeling Enhancements § 2-eqn. Turbulence model § , models with standard and Launder-Spalding wall functions § Exact boundary condition imposition § Training features § Support for new optimizers § 30+ optimizers § New algorithms for loss balancing § Grad Norm, Relative Loss Balancing with Random Lookback, and Soft Adapt § Sobolev (gradient-enhanced) training § Hydra Config § Post-processing <latexit sha1_base64="FULNvxR0CTA5RmKEYCXKafsNPCc=">AAAB+3icbVDLSgNBEOz1GeMr6tHLYhC8GHYlqMegF48RzAOSJcxOepMxszPLzKwYQn7Fi4giXv0Rb/6Nk2QPmljQUFR1090VJpxp43nfztLyyuraem4jv7m1vbNb2Nuva5kqijUquVTNkGjkTGDNMMOxmSgkccixEQ6uJ37jAZVmUtyZYYJBTHqCRYwSY6V7GMApvABCAhoYcJAgOoWiV/KmcBeJn5EiZKh2Cl/trqRpjMJQTrRu+V5ighFRhlGO43w71ZgQOiA9bFkqSIw6GE1vH7vHVum6kVS2hHGn6u+JEYm1Hsah7YyJ6et5byL+57VSE10GIyaS1KCgs0VRyl0j3UkQbpcppIYPLSFUMXurS/tEEWpsXHkbgj//8iKpn5X881L5tlysXGVx5OAQjuAEfLiACtxAFWpA4RGe4BXenLHz7Lw7H7PWJSebOYA/cD5/AIQQkYg=</latexit> k ✏ <latexit sha1_base64="q+OthTPT4zzYsSYxJtVSkuO79OE=">AAAB93icbVDJSgNBEK1xjXGLevTSGAQvhhkJ6jHoxWMEs0AyhJ5OT9Kkl6G7RwhDfsSLBxe8+ive/Bs7yRw08UHB470qqupFCWfG+v63t7K6tr6xWdgqbu/s7u2XDg6bRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0O/Vbj1QbpuSDHSc0FHggWcwItk4awgjO4Q0UCKAwANwrlf2KPwNaJkFOypCj3it9dfuKpIJKSzg2phP4iQ0zrC0jnE6K3dTQBJMRHtCOoxILasJsdvcEnTqlj2KlXUmLZurviQwLY8Yicp0C26FZ9Kbif14ntfF1mDGZpJZKMl8UpxxZhaYhoD7TlFg+dgQTzdytiAyxxsS6qIouhGDx5WXSvKgEl5XqfbVcu8njKMAxnMAZBHAFNbiDOjSAgIUneIFXb+w9e+/ex7x1xctnjuAPvM8fd2aQcQ==</latexit> k !
- 31. LERN MORE GTC2022 sessions § Getting Started with AI for Engineering Simulations using Modulus on Rescale Platform [S42087] § Case Study on Developing Digital Twins for the Power Industry using Modulus and Omniverse [S41671] § Developing Digital Twins for Energy Applications using Modulus [S41325] § Developing Digital Twins for Weather, Climate, and Energy [S41823] NVIDIA Modulus documentation § https://docs.nvidia.com/deeplearning/modulus/index.html Blog § Siemens Energy Taps NVIDIA to Develop Industrial Digital Twin of Power Plant in Omniverse
- 32. LERN MORE Blog § Accelerating Product Development with Physics-Informed Neural Networks and NVIDIA Modulus § Using Hybrid Physics-Informed Neural Networks for Digital Twins in Prognosis and Health Management § Using Physics-Informed Deep Learning for Transport in Porous Media