Roberto Castilla López

A variational formulation for the multilayer perceptron

In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for the multilayer perceptron provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique we use a multilayer perceptron to solve some classical problems in the calculus of variations.

A novel fabrication technique to minimize poly(dimethylsiloxane)-microchannels deformation under high-pressure operation.

PDMS is one of the most common materials used for the flow delivery in the microfluidics chips, since it is clear, inert, nontoxic, and nonflammable. Its inexpensiveness, straightforward fabrication, and biological compatibility have made it a favorite material in the exploratory stages of the bio‐microfluidic devices. If small footprint assays want to be performed while keeping the throughput, high pressure‐rated channels should be used, but PDMS flexibility causes an important issue since it can generate a large variation of microchannel geometry. In this work, a novel fabrication technique based on the prevention of PDMS deformation is developed. A photo‐sensible thiolene resin (Norland Optical Adhesive 63, NOA 63) is used to create a rigid coating layer over the stiff PDMS micropillar array, which significantly reduces the pressure‐induced shape changes. This method uses the exact same soft lithography manufacturing equipment. The verification of the presented technique was investigated experimentally and numerically and the manufactured samples showed a deformation 70% lower than PDMS conventional samples.

An extended class of multilayer perceptron

In this work an extended class of multilayer perceptron is presented. This includes independent parameters, boundary conditions and lower and upper bounds. In some cases, such extensions contain a priori information of the problem. On some other situations they are necessary in order to define a correct representation for the solution. The use of this augmented class of neural network is illustrated through a case study in the optimal control theory. The numerical results are compared against the analytical solution.