@@ -82,10 +82,10 @@ import ufl
8282import numpy as np
8383import sys, os
8484sys.path.append(os.environ.get(' HIPPYLIB_PATH' ))
85- from hippylib import *
85+ import hippylib as hp
8686
8787sys.path.append(os.environ.get(' HIPPYFLOW_PATH' ))
88- from hippyflow import *
88+ import hippyflow as hf
8989
9090# Set up PDE Variational Problem and observable using a function
9191def build_observable (mesh , ** kwargs ):
@@ -96,16 +96,19 @@ def build_observable(mesh, **kwargs):
9696 Vh = [Vh2, Vh1, Vh2]
9797 # Initialize Expressions
9898 f = dl.Constant(0.0 )
99+
100+ def u_boundary (x ,on_boundary ):
101+ return on_boundary
99102
100103 u_bdr = dl.Expression(" x[1]" , degree = 1 )
101104 u_bdr0 = dl.Constant(0.0 )
102- bc = dl.DirichletBC(Vh[STATE ], u_bdr, u_boundary)
103- bc0 = dl.DirichletBC(Vh[STATE ], u_bdr0, u_boundary)
105+ bc = dl.DirichletBC(Vh[hp. STATE ], u_bdr, u_boundary)
106+ bc0 = dl.DirichletBC(Vh[hp. STATE ], u_bdr0, u_boundary)
104107
105108 def pde_varf (u ,m ,p ):
106109 return ufl.exp(m)* ufl.inner(ufl.grad(u), ufl.grad(p))* ufl.dx - f* p* ufl.dx
107110
108- pde = PDEVariationalProblem(Vh, pde_varf, bc, bc0, is_fwd_linear = True )
111+ pde = hp. PDEVariationalProblem(Vh, pde_varf, bc, bc0, is_fwd_linear = True )
109112
110113 # Instance observable operator (in this case pointwise observation of state)
111114 x_targets = np.linspace(0.1 ,0.9 ,10 )
@@ -116,8 +119,8 @@ def build_observable(mesh, **kwargs):
116119 targets.append((xi,yi))
117120 targets = np.array(targets)
118121
119- B = assemblePointwiseObservation(Vh[STATE ], targets)
120- return LinearStateObservable(pde,B)
122+ B = hp. assemblePointwiseObservation(Vh[hp. STATE ], targets)
123+ return hf. LinearStateObservable(pde,B)
121124
122125# Set up mesh
123126ndim = 2
@@ -129,15 +132,15 @@ observable_kwargs = {} # No kwargs given in this example
129132observable = build_observable(mesh,** observable_kwargs)
130133
131134# Instance probability distribution for the parameter
132- prior = BiLaplacian2D(Vh[PARAMETER ],gamma = 0.1 , delta = 1.0 )
135+ prior = hp. BiLaplacian2D(observable.problem. Vh[hp. PARAMETER ],gamma = 0.1 , delta = 1.0 )
133136
134137# Instance Active Subspace Operator
135- AS = ActiveSubspaceProjector(observable,prior)
138+ AS = hf. ActiveSubspaceProjector(observable,prior)
136139# Compute and save input reduced basis to file:
137140AS .construct_input_subspace()
138141
139142# Instance POD Operator to compute POD basis and training data
140- POD = PODProjector(observable,prior)
143+ POD = hf. PODProjector(observable,prior)
141144POD .construct_subspace()
142145output_directory = ' location/for/training/data/'
143146POD .generate_training_data(output_directory)
@@ -181,7 +184,7 @@ These publications use the hippyflow library
181184
182185[ ** Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs** ] ( https://www.sciencedirect.com/science/article/pii/S0045782521005302 ) .
183186Computer Methods in Applied Mechanics and Engineering. Volume 388, 1 January 2022, 114199.
184- ([ Download] ( https://arxiv.org/pdf/2011.15110.pdf ) )<details ><summary >BibTeX</summary ><pre >
187+ ([ Download] ( https://www.sciencedirect.com/science/article/pii/S0045782521005302 ) )<details ><summary >BibTeX</summary ><pre >
185188@article {OLearyRoseberryVillaChenEtAl2022,
186189 title={Derivative-informed projected neural networks for high-dimensional parametric maps governed by {PDE}s},
187190 author={O’Leary-Roseberry, Thomas and Villa, Umberto and Chen, Peng and Ghattas, Omar},
@@ -194,14 +197,46 @@ Computer Methods in Applied Mechanics and Engineering. Volume 388, 1 January 202
194197}</pre ></details >
195198
196199- \[ 2\] O'Leary-Roseberry, T., Du, X., Chaudhuri, A., Martins, J., Willcox, K., Ghattas, O.,
197- [ ** Adaptive Projected Residual Networks for Learning Parametric Maps from Sparse Data** ] ( https://arxiv.org/abs/2112.07096 ) .
198- arXiv:2112.07096.
199- ([ Download] ( https://arxiv.org/pdf/2112.07096.pdf ) )<details ><summary >BibTeX</summary ><pre >
200- @article {OLearyRoseberryDuChaudhuriEtAl2021,
201- title={Adaptive Projected Residual Networks for Learning Parametric Maps from Sparse Data},
202- author={O'Leary-Roseberry, Thomas and Du, Xiaosong, and Chaudhuri, Anirban, and Martins Joaqium R. R. A., and Willcox, Karen, and Ghattas, Omar},
203- journal={arXiv preprint arXiv:2112.07096},
204- year={2021}
200+ [ ** Learning high-dimensional parametric maps via reduced basis adaptive residual networks** ] ( https://www.sciencedirect.com/science/article/abs/pii/S0045782522006855 ) .
201+ Computer Methods in Applied Mechanics and Engineering. Volume 402, December 2022, 115730.
202+ ([ Download] ( https://www.sciencedirect.com/science/article/abs/pii/S0045782522006855 ) )<details ><summary >BibTeX</summary ><pre >
203+ @article {OLearyRoseberryDuChaudhuriEtAl2022,
204+ title={Learning high-dimensional parametric maps via reduced basis adaptive residual networks},
205+ author={O’Leary-Roseberry, Thomas and Du, Xiaosong and Chaudhuri, Anirban and Martins, Joaquim RRA and Willcox, Karen and Ghattas, Omar},
206+ journal={Computer Methods in Applied Mechanics and Engineering},
207+ volume={402},
208+ pages={115730},
209+ year={2022},
210+ publisher={Elsevier}
211+ }
212+ }</pre ></details >
213+
214+ - \[ 3\] Wu, K., O'Leary-Roseberry, T., Chen, P., Ghattas, O.,
215+ [ ** Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network** ] ( https://link.springer.com/article/10.1007/s10915-023-02145-1 ) .
216+ Journal of Scientific Computing 95. Article number: 30 (2023)
217+ ([ Download] ( https://link.springer.com/article/10.1007/s10915-023-02145-1 ) )<details ><summary >BibTeX</summary ><pre >
218+ @article {WuOLearyRoseberryChenEtAl2023,
219+ title={Large-Scale {B}ayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network},
220+ author={Wu, Keyi and O’Leary-Roseberry, Thomas and Chen, Peng and Ghattas, Omar},
221+ journal={Journal of Scientific Computing},
222+ volume={95},
223+ number={1},
224+ pages={30},
225+ year={2023},
226+ publisher={Springer}
205227}
206228}</pre ></details >
207229
230+ - \[ 4\] Cao, L., O'Leary-Roseberry, T., Jha, P., Oden, J.T., Ghattas, O.,
231+ [ ** Residual-Based Error Correction for Neural Operator Accelerated Infinite-Dimensional Bayesian Inverse Problems** ] ( https://www.sciencedirect.com/science/article/pii/S0021999123001997 ) .
232+ Journal of Computational Physics, 112104
233+ ([ Download] ( https://www.sciencedirect.com/science/article/pii/S0021999123001997 ) )<details ><summary >BibTeX</summary ><pre >
234+ @article {CaoOLearyRoseberryJhaEtAl2023,
235+ title={Residual-based error correction for neural operator accelerated infinite-dimensional {B}ayesian inverse problems},
236+ author={Cao, Lianghao and O'Leary-Roseberry, Thomas and Jha, Prashant K and Oden, J Tinsley and Ghattas, Omar},
237+ journal={Journal of Computational Physics},
238+ pages={112104},
239+ year={2023},
240+ publisher={Elsevier}
241+ }
242+ }</pre ></details >
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