AnisotropicGBEnergy

Evaluates anisotropic grain-boundary energy from a TorchScript model.

AnisotropicGBEnergy evaluates a TorchScript model on grain-boundary normal vectors and stores both the resulting scalar grain-boundary energy and its derivative with respect to the incoming normal tensor in output buffers.

Overview

The object expects gb_gradient_buffer, a vector-valued tensor buffer with trailing component dimension 3, typically generated by GradientVector. The input is flattened to (N, 3), normalized row-wise,

$var element = document.getElementById("moose-equation-e8555f26-5494-4277-86b3-0e8b963be473");katex.render("\\hat{n} = \\frac{\\nabla \\eta}{|\\nabla \\eta|}", element, {displayMode:true,throwOnError:false});$

and passed to the TorchScript module to obtain the grain-boundary energy $var element = document.getElementById("moose-equation-4c74209c-8f02-4afa-9779-48408ac9c6c8");katex.render("\\gamma(\\hat{n})", element, {displayMode:false,throwOnError:false});$ , written to the buffer output. Autograd is used to additionally compute $var element = document.getElementById("moose-equation-91cfbc88-adc1-476a-8ef7-68cfb2d6e09f");katex.render("d\\gamma/d(\\nabla \\eta)", element, {displayMode:false,throwOnError:false});$ , written to the dsigma_dn output buffer with the same shape as gb_gradient_buffer.

Only points where $var element = document.getElementById("moose-equation-e13632c6-b72b-4ce3-b43f-9432b291e210");katex.render("|\\nabla \\eta|", element, {displayMode:false,throwOnError:false});$ clears a gradient-magnitude threshold are passed to the model. For a $var element = document.getElementById("moose-equation-c9767851-bf3e-40fb-819c-7f4071bcc744");katex.render("\\tanh", element, {displayMode:false,throwOnError:false});$ interface profile of width interface_width ( $var element = document.getElementById("moose-equation-b5c83021-3f54-46d6-a9c2-263c01045814");katex.render("W", element, {displayMode:false,throwOnError:false});$ ), the threshold is

$var element = document.getElementById("moose-equation-0dbb526c-f5b3-456d-811c-605ae1dd99d3");katex.render("|\\nabla \\eta|_{\\mathrm{thresh}} = \\frac{2}{W \\cosh^2(4)}", element, {displayMode:true,throwOnError:false});$

which is negligible one interface width from the boundary. Outside this masked region, dsigma_dn is zero (there is no boundary to differentiate), while the energy buffer is filled with the largest energy value measured anywhere in the domain (or 1.0 if no interface point was found anywhere), to avoid introducing an artificial low-energy region in the bulk.

In two dimensions, GradientVector zero-pads the third (z) component of the gradient, so the model receives normals of the form $var element = document.getElementById("moose-equation-a78035a4-22c3-4010-a0ef-a18f36915c7f");katex.render("(\\nabla_x \\eta, \\nabla_y \\eta, 0)", element, {displayMode:false,throwOnError:false});$ and must be trained (or otherwise tolerant of) this convention.

Example Input File Syntax

[TensorComputes<<<{"href": "../../syntax/TensorComputes/index.html"}>>>]
  [Solve<<<{"href": "../../syntax/TensorComputes/Solve/index.html"}>>>]
    [gb_energy]
      type = AnisotropicGBEnergy<<<{"description": "Evaluates anisotropic grain-boundary energy from a TorchScript model.", "href": "AnisotropicGBEnergy.html"}>>>
      buffer<<<{"description": "The buffer this compute is writing to"}>>> = gb_energy
      gb_gradient_buffer<<<{"description": "Input tensor buffer containing grain-boundary gradient vectors."}>>> = grad_eta
      dsigma_dn<<<{"description": "Output tensor buffer for the derivative of GB energy with respect to the normal tensor."}>>> = dsigma_dn
      libtorch_model_file<<<{"description": "Path to the TorchScript file containing the GB energy model."}>>> = 'marlin:anisotropic_gb_energy/analytic_sigma.pt'
      interface_width<<<{"description": "Coarsest interface width in model."}>>> = ${interface_width}
      chunk_size<<<{"description": "Maximum number of spatial points processed at once. Smaller values reduce peak GPU memory usage at the cost of additional TorchScript launches."}>>> = 256
    []
  []
[]

Input Parameters

bufferThe buffer this compute is writing to
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to
dsigma_dnOutput tensor buffer for the derivative of GB energy with respect to the normal tensor.
C++ Type:std::string
Controllable:No
Description:Output tensor buffer for the derivative of GB energy with respect to the normal tensor.
gb_gradient_bufferInput tensor buffer containing grain-boundary gradient vectors.
C++ Type:std::string
Controllable:No
Description:Input tensor buffer containing grain-boundary gradient vectors.
interface_widthCoarsest interface width in model.
C++ Type:Real
Unit:(no unit assumed)
Range:interface_width > 0
Controllable:No
Description:Coarsest interface width in model.
libtorch_model_filePath to the TorchScript file containing the GB energy model.
C++ Type:DataFileName
Controllable:No
Description:Path to the TorchScript file containing the GB energy model.

Required Parameters

chunk_size65536Maximum number of spatial points processed at once. Smaller values reduce peak GPU memory usage at the cost of additional TorchScript launches.
Default:65536
C++ Type:unsigned int
Range:chunk_size > 0
Controllable:No
Description:Maximum number of spatial points processed at once. Smaller values reduce peak GPU memory usage at the cost of additional TorchScript launches.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/anisotropic_grain_growth/analytic_hull.i)

(test/tests/anisotropic_grain_growth/analytic_hull.i)

interface_width = 0.8
r0 = 4

gbe_max = ${units 0.8 J/m^2}
kappa = ${fparse 0.75 * gbe_max * interface_width}
L = 1

g_eta_expr = '(eta^2*(1-eta^2)^2)'

[Domain]
  dim = 2
  nx = 32
  ny = 32
  xmax = 16
  ymax = 16
  mesh_mode = DUMMY
  floating_precision = SINGLE
[]

[TensorComputes]
  [Initialize]
    [eta]
      type = ParsedCompute
      buffer = 'eta'
      extra_symbols = 'true'
      expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2);0.5 - 0.5*tanh(2*(radius-${r0})/${interface_width})'
    []
    [kappa_linear_term]
      type = ReciprocalLaplacianFactor
      buffer = kappa_linear_term
      factor = ${fparse ${L} * ${kappa}}
    []
    [smooth]
      type = DeAliasingTensor
      method = HOULI
      buffer = smooth
    []
  []
  [Solve]
    [grad_eta_vector]
      type = GradientVector
      buffer = grad_eta
      input = eta
    []
    [gb_energy]
      type = AnisotropicGBEnergy
      buffer = gb_energy
      gb_gradient_buffer = grad_eta
      dsigma_dn = dsigma_dn
      libtorch_model_file = 'marlin:anisotropic_gb_energy/analytic_sigma.pt'
      interface_width = ${interface_width}
      chunk_size = 256
    []
    [bulk_driving_force]
      type = ParsedCompute
      buffer = 'bulk_driving_force'
      expression = '6 * gb_energy * ${g_eta_expr} / ${interface_width}'
      inputs = 'mu eta gb_energy'
      derivatives = 'eta'
    []
    [dmu_dn]
      type = ParsedCompute
      buffer = 'dmu_dn'
      expression = '6 * dsigma_dn / ${interface_width}'
      inputs = 'dsigma_dn'
    []
    [g]
      type = ParsedCompute
      buffer = 'g'
      expression = '${g_eta_expr}'
      inputs = 'eta'
    []
    [anisotropy_torque]
      type = AnisotropyTorque
      buffer = anisotropy_torque
      dmu_dn = dmu_dn
      g = g
    []
    [total_mu_driving_force]
      type = ParsedCompute
      buffer = 'total_mu_driving_force'
      expression = '-${L}*(bulk_driving_force - anisotropy_torque)'
      inputs = 'bulk_driving_force anisotropy_torque'
    []

    [nonlinear]
      type = ForwardFFT
      buffer = 'NL'
      input = 'total_mu_driving_force'
    []
    [smooth_nonlinear]
      type = ParsedCompute
      buffer = 'smooth_NL'
      expression = 'smooth * NL'
      inputs = 'smooth NL'
    []

    [etabar]
      type = ForwardFFT
      buffer = etabar
      input = eta
    []

    [gradient_energy]
      type = GradientEnergyDensity
      buffer = gradient_energy
      gradient_buffers = 'grad_eta'
      kappa = ${kappa}
    []

    [interface_energy]
      type = ParsedCompute
      buffer = interface_energy
      expression = 'g * 6 * gb_energy / ${interface_width} + gradient_energy'
      inputs = 'g gb_energy gradient_energy'
    []
  []
[]

[TensorSolver]
  type = AdamsBashforthMoulton
  buffer = 'eta'
  reciprocal_buffer = 'etabar'
  linear_reciprocal = 'kappa_linear_term'
  nonlinear_reciprocal = 'smooth_NL'
  substeps = 1e2
  predictor_order = 1
  corrector_order = 1
  corrector_steps = 1
[]

[Postprocessors]
  [total_gb_energy]
    type = TensorIntegralPostprocessor
    buffer = interface_energy
  []
[]

[TensorOutputs]
  active = ''
  [xdmf]
    type = XDMFTensorOutput
    buffer = 'eta gb_energy'
    output_mode = 'NODE NODE'
    enable_hdf5 = true
    transpose = false
  []
[]

[Executioner]
  type = Transient
  dt = 0.1
  num_steps = 2
[]

[Outputs]
  csv = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

(test/tests/anisotropic_grain_growth/analytic_hull.i)

interface_width = 0.8
r0 = 4

gbe_max = ${units 0.8 J/m^2}
kappa = ${fparse 0.75 * gbe_max * interface_width}
L = 1

g_eta_expr = '(eta^2*(1-eta^2)^2)'

[Domain]
  dim = 2
  nx = 32
  ny = 32
  xmax = 16
  ymax = 16
  mesh_mode = DUMMY
  floating_precision = SINGLE
[]

[TensorComputes]
  [Initialize]
    [eta]
      type = ParsedCompute
      buffer = 'eta'
      extra_symbols = 'true'
      expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2);0.5 - 0.5*tanh(2*(radius-${r0})/${interface_width})'
    []
    [kappa_linear_term]
      type = ReciprocalLaplacianFactor
      buffer = kappa_linear_term
      factor = ${fparse ${L} * ${kappa}}
    []
    [smooth]
      type = DeAliasingTensor
      method = HOULI
      buffer = smooth
    []
  []
  [Solve]
    [grad_eta_vector]
      type = GradientVector
      buffer = grad_eta
      input = eta
    []
    [gb_energy]
      type = AnisotropicGBEnergy
      buffer = gb_energy
      gb_gradient_buffer = grad_eta
      dsigma_dn = dsigma_dn
      libtorch_model_file = 'marlin:anisotropic_gb_energy/analytic_sigma.pt'
      interface_width = ${interface_width}
      chunk_size = 256
    []
    [bulk_driving_force]
      type = ParsedCompute
      buffer = 'bulk_driving_force'
      expression = '6 * gb_energy * ${g_eta_expr} / ${interface_width}'
      inputs = 'mu eta gb_energy'
      derivatives = 'eta'
    []
    [dmu_dn]
      type = ParsedCompute
      buffer = 'dmu_dn'
      expression = '6 * dsigma_dn / ${interface_width}'
      inputs = 'dsigma_dn'
    []
    [g]
      type = ParsedCompute
      buffer = 'g'
      expression = '${g_eta_expr}'
      inputs = 'eta'
    []
    [anisotropy_torque]
      type = AnisotropyTorque
      buffer = anisotropy_torque
      dmu_dn = dmu_dn
      g = g
    []
    [total_mu_driving_force]
      type = ParsedCompute
      buffer = 'total_mu_driving_force'
      expression = '-${L}*(bulk_driving_force - anisotropy_torque)'
      inputs = 'bulk_driving_force anisotropy_torque'
    []

    [nonlinear]
      type = ForwardFFT
      buffer = 'NL'
      input = 'total_mu_driving_force'
    []
    [smooth_nonlinear]
      type = ParsedCompute
      buffer = 'smooth_NL'
      expression = 'smooth * NL'
      inputs = 'smooth NL'
    []

    [etabar]
      type = ForwardFFT
      buffer = etabar
      input = eta
    []

    [gradient_energy]
      type = GradientEnergyDensity
      buffer = gradient_energy
      gradient_buffers = 'grad_eta'
      kappa = ${kappa}
    []

    [interface_energy]
      type = ParsedCompute
      buffer = interface_energy
      expression = 'g * 6 * gb_energy / ${interface_width} + gradient_energy'
      inputs = 'g gb_energy gradient_energy'
    []
  []
[]

[TensorSolver]
  type = AdamsBashforthMoulton
  buffer = 'eta'
  reciprocal_buffer = 'etabar'
  linear_reciprocal = 'kappa_linear_term'
  nonlinear_reciprocal = 'smooth_NL'
  substeps = 1e2
  predictor_order = 1
  corrector_order = 1
  corrector_steps = 1
[]

[Postprocessors]
  [total_gb_energy]
    type = TensorIntegralPostprocessor
    buffer = interface_energy
  []
[]

[TensorOutputs]
  active = ''
  [xdmf]
    type = XDMFTensorOutput
    buffer = 'eta gb_energy'
    output_mode = 'NODE NODE'
    enable_hdf5 = true
    transpose = false
  []
[]

[Executioner]
  type = Transient
  dt = 0.1
  num_steps = 2
[]

[Outputs]
  csv = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

Overview
Example Input File Syntax
Input Parameters
Input Files