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Docs unification (#260)
* move some elements to unified docs, re-organize * make all paths relative * cleanup * fix broken links * doc fixes * fix docutils issues * minor doc updates * update * black
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docs/api/api_index.rst

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Welcome to the PhysicsNeMo Sym API documentation.
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Fundamental API
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================
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docs/api_index.rst

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API Reference
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==================
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API documentation for PhysicsNeMo Sym.
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.. toctree::
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:maxdepth: 2
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:caption: PhysicsNeMo Sym API
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:name: PhysicsNeMo Sym API
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api/api_index

docs/examples_index.rst

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Examples
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============================
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Examples using PhysicsNeMo Sym
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.. toctree::
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:maxdepth: 1
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:caption: Basics
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:name: Basics
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user_guide/basics/lid_driven_cavity_flow.rst
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.. toctree::
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:maxdepth: 1
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:caption: Physics-Informed Foundations
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:name: Physics-Informed Foundations
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user_guide/foundational/1d_wave_equation.rst
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user_guide/foundational/2d_wave_equation.rst
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user_guide/foundational/ode_spring_mass.rst
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user_guide/foundational/zero_eq_turbulence.rst
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user_guide/foundational/scalar_transport.rst
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user_guide/foundational/linear_elasticity.rst
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user_guide/foundational/inverse_problem.rst
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.. toctree::
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:maxdepth: 1
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:caption: Neural Operators
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:name: Neural Operators
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user_guide/neural_operators/darcy_fno.rst
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user_guide/neural_operators/darcy_afno.rst
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user_guide/neural_operators/darcy_pino.rst
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user_guide/neural_operators/deeponet.rst
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.. toctree::
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:maxdepth: 1
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:caption: Intermediate Case Studies
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:name: Intermediate Case Studies
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user_guide/intermediate/variational_example.rst
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user_guide/intermediate/adding_stl_files.rst
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user_guide/intermediate/moving_time_window.rst
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user_guide/intermediate/em.rst
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user_guide/intermediate/two_equation_turbulent_channel.rst
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user_guide/intermediate/turbulence_super_resolution.rst
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.. toctree::
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:maxdepth: 1
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:caption: Advanced Case Studies
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:name: Advanced Case Studies
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user_guide/advanced/conjugate_heat_transfer.rst
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user_guide/advanced/parametrized_simulations.rst
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user_guide/advanced/2d_heat_transfer.rst
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user_guide/advanced/fpga.rst
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user_guide/advanced/industrial_heat_sink.rst
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docs/features_index.rst

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PhysicsNeMo Sym Features
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========================
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Core features and capabilities of PhysicsNeMo Sym.
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.. toctree::
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:maxdepth: 1
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:caption: PhysicsNeMo Sym Features
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:name: PhysicsNeMo Sym Features
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user_guide/features/csg_and_tessellated_module.rst
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user_guide/features/nodes.rst
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user_guide/features/constraints.rst
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user_guide/features/configuration.rst
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user_guide/features/post_processing.rst
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user_guide/features/performance.rst
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docs/index.rst

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********************************************
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NVIDIA PhysicsNeMo Sym (Latest Release)
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********************************************
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..
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TODO: add conf.py and root_doc
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NVIDIA PhysicsNeMo Sym is a deep learning framework that blends the power of
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physics and partial differential equations (PDEs) with AI to build more
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robust models for better analysis.
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There is a plethora of ways in which ML/NN models can be applied for
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physics-based systems. These can depend based on the availability of
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observational data and the extent of understanding of underlying physics.
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Based on these aspects, the ML/NN based methodologies can be broadly
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classified into forward (physics-driven), data-driven and hybrid approaches
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that involve both the physics and data assimilation.
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.. figure:: /images/user_guide/ai_in_computational_sciences_spectrum.png
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:alt: AI in computational sciences
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:width: 80.0%
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:align: center
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With NVIDIA PhysicsNeMo Sym, we aim to provide researchers and industry specialists,
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various tools that will help accelerate your development of such models for the
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scientific discipline of your need. Experienced users can start with exploring the
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PhysicsNeMo Sym APIs and building the models while beginners can use this User Guide
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as a portal to explore the possibilities of AI in the domain of scientific
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computation. The User Guide comes in with several examples that will help
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you jumpstart your development of AI driven models.
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PhysicsNeMo Sym
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===============
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.. toctree::
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:maxdepth: 2
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:caption: Learn the Basics
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:name: Learn the Basics
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:hidden:
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Overview <user_guide/basics/physicsnemo_overview.rst>
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Introductory Example <user_guide/basics/lid_driven_cavity_flow.rst>
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.. toctree::
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:maxdepth: 1
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:caption: Theory
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:name: Theory
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:hidden:
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Physics-Informed Learning <user_guide/theory/phys_informed.rst>
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Architectures <user_guide/theory/architectures.rst>
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Advanced Schemes <user_guide/theory/advanced_schemes.rst>
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Recommended Practices <user_guide/theory/recommended_practices.rst>
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Miscellaneous Concepts <user_guide/theory/miscellaneous.rst>
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.. toctree::
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:maxdepth: 1
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:caption: PhysicsNeMo Sym Features
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:name: PhysicsNeMo Sym Features
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:hidden:
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Geometry and Tesselation Modules <user_guide/features/csg_and_tessellated_module.rst>
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Computational Graph, Nodes and Architectures <user_guide/features/nodes.rst>
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Constraints <user_guide/features/constraints.rst>
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Configuration <user_guide/features/configuration.rst>
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Post Processing <user_guide/features/post_processing.rst>
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Performance <user_guide/features/performance.rst>
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:caption: Contents
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:name: Contents
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.. toctree::
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:maxdepth: 1
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:caption: Physics-Informed Foundations
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:name: Physics-Informed Foundations
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:hidden:
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1D Wave Equation <user_guide/foundational/1d_wave_equation.rst>
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2D Wave Equation <user_guide/foundational/2d_wave_equation.rst>
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Spring Mass ODE <user_guide/foundational/ode_spring_mass.rst>
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Zero Equation Turbulence <user_guide/foundational/zero_eq_turbulence.rst>
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Scalar Transport <user_guide/foundational/scalar_transport.rst>
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Linear Elasticity <user_guide/foundational/linear_elasticity.rst>
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Inverse Problem <user_guide/foundational/inverse_problem.rst>
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.. toctree::
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:maxdepth: 1
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:caption: Neural Operators
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:name: Neural Operators
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:hidden:
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Fourier <user_guide/neural_operators/darcy_fno.rst>
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Adaptive Fourier <user_guide/neural_operators/darcy_afno.rst>
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Physics-Informed <user_guide/neural_operators/darcy_pino.rst>
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Deep-O Nets <user_guide/neural_operators/deeponet.rst>
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FourCastNet <user_guide/neural_operators/fourcastnet.rst>
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.. toctree::
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:maxdepth: 1
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:caption: Intermediate Case Studies
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:name: Intermediate Case Studies
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:hidden:
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Variational Examples <user_guide/intermediate/variational_example.rst>
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Geometry from STL Files <user_guide/intermediate/adding_stl_files.rst>
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Time Window Training <user_guide/intermediate/moving_time_window.rst>
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Electromagnetics <user_guide/intermediate/em.rst>
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2D Turbulent Channel <user_guide/intermediate/two_equation_turbulent_channel.rst>
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Turbulence Super Resolution <user_guide/intermediate/turbulence_super_resolution.rst>
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.. toctree::
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:maxdepth: 1
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:caption: Advanced Case Studies
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:name: Advanced Case Studies
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:hidden:
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Conjugate Heat Transfer <user_guide/advanced/conjugate_heat_transfer.rst>
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3D Fin Parameterization <user_guide/advanced/parametrized_simulations.rst>
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Heat Transfer with High Conductivity <user_guide/advanced/2d_heat_transfer.rst>
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FPGA <user_guide/advanced/fpga.rst>
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Industrial Heat Sink <user_guide/advanced/industrial_heat_sink.rst>
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.. toctree::
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:maxdepth: 2
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:caption: PhysicsNeMo Sym API
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:name: PhysicsNeMo Sym API
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:hidden:
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api/api_index
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theory_index
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features_index
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examples_index
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api_index

docs/theory_index.rst

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Theory
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======
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Theoretical foundations and concepts behind PhysicsNeMo Sym.
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.. toctree::
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:maxdepth: 1
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:caption: Theory
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:name: Theory
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user_guide/theory/phys_informed.rst
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user_guide/theory/architectures.rst
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user_guide/theory/advanced_schemes.rst
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user_guide/theory/recommended_practices.rst
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user_guide/theory/miscellaneous.rst

docs/user_guide/advanced/2d_heat_transfer.rst

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The geometry of the problem is a simple composite 2D geometry with different material conductivities. The heat source is placed in inside the material of higher conductivity to replicate the actual heatsink and scenario. The objective of this case is to mimic the orders of magnitude difference between Copper :math:`(k=385 \text{ } W/m-K)` and Air :math:`(k=0.0261 \text{ } W/m-K)`. Therefore, set the conductivity of the heatsink and surrounding solid to 100 and 0.01 respectively.
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.. figure:: /images/user_guide/2d-solid-solid-geo.png
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.. figure:: ../../images/user_guide/2d-solid-solid-geo.png
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:alt: Geometry for 2D solid-solid case
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This figure visualizes the solution.
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.. figure:: /images/user_guide/2d_solid_solid_results.png
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.. figure:: ../../images/user_guide/2d_solid_solid_results.png
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:alt: Results for 2D solid-solid case
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geometry are more representative of a real heatsink geometry scales. The real properties for air and copper will also be used in this example. This example is also a
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good demonstrator for nondimensionalizing the properties/geometries to improve the neural network training. This figure shows the geometry and measurements for this problem.
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.. figure:: /images/user_guide/solid_fluid_geo.png
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.. figure:: ../../images/user_guide/solid_fluid_geo.png
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at the interface when compared to the commercial solution. We believe these differences in the solver results are due to the discretization errors and can be potentially fixed
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by improving the grid resolution at the interface. PhysicsNeMo Sym prediction however does not suffer from such errors and the physical constraints are respected to a better degree of accuracy.
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.. figure:: /images/user_guide/2d_solid_fluid_results.png
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.. figure:: ../../images/user_guide/2d_solid_fluid_results.png
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:alt: Results for 2D solid-fluid case
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:width: 99.0%
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