> C. Ruyer-Quil
Adaptive Deep Convolutional Neural Networks and Supervised Learning for the Solution of Direct and Inverse Engineering Problems
Bijan Mohammadi (Univ. Montpellier)
We present an original deep convolutional neural network (DCNN) implementation and its applications in learning for several engineering direct and inverse problems. Our DCNN permits to detect and learn existing relationships between data basis provided by the user. It builds approximations for either the forward or inverse problems. The former appears especially useful for the initialization of optimization algorithms.
Having in hand a data basis of x in Rn --> J in Rm,
the procedure builds a network with a adaptative number of hidden layers and hidden variables and weights. It uses available information in learning for:
1-Choice of the convolution kernel where typical kernel are non-isotropic, non-symmetric Gaussian kernels: d(A,B)=exp(-((A-B)t Mi (A-B))pi) at layer i
2-Parameters Y=(wi,Mi,pi) of the kernel by back-propagation (with stochastic gradient methods or adjoint based) where the number of epochs (iterations) is not a priori fixed.
Find Y s.t. GradYJ(X,Y)=0 @ given X with J= CNN/DATA misfit,
GradYJ(X,Y) by Automatic Differentiation of the CNN
3- Number of layers, not a priori fixed.
Once the DCNN built, it can also be used in inverse problems with gradient-based algorithms using surrogate gradient GradXJ(X,Y) @ given Y starting from an initialization by the Reverse CNN.
Of course, direct and reverse uncertainty propagations using Monte Carlo approaches become then feasible.
We show the application of the approach to various engineering/environmental/medical problems.