Lalita Udpa | PubMed Health

PubMed2005

Finite-element neural networks for solving differential equations.

The solution of partial differential equations (PDE) arises in a wide variety of engineering problems. Solutions to most practical problems use numerical analysis techniques such as finite-element or finite-difference methods. The drawbacks of these approaches include computational costs associated with the modeling of complex geometries. This paper proposes a finite-element neural network (FENN) obtained by embedding a finite-element model in a neural network architecture that enables fast and accurate solution of the forward problem. Results of applying the FENN to several simple electromagnetic forward and inverse problems are presented. Initial results indicate that the FENN performance as a forward model is comparable to that of the conventional finite-element method (FEM). The FENN can also be used in an iterative approach to solve inverse problems associated with the PDE. Results showing the ability of the FENN to solve the inverse problem given the measured signal are also presented. The parallel nature of the FENN also makes it an attractive solution for parallel implementation in hardware and software.

Algorithms↗

PubMed2004

An incremental learning algorithm with confidence estimation for automated identification of NDE signals.

An incremental learning algorithm is introduced for learning new information from additional data that may later become available, after a classifier has already been trained using a previously available database. The proposed algorithm is capable of incrementally learning new information without forgetting previously acquired knowledge and without requiring access to the original database, even when new data include examples of previously unseen classes. Scenarios requiring such a learning algorithm are encountered often in nondestructive evaluation (NDE) in which large volumes of data are collected in batches over a period of time, and new defect types may become available in subsequent databases. The algorithm, named Learn++, takes advantage of synergistic generalization performance of an ensemble of classifiers in which each classifier is trained with a strategically chosen subset of the training databases that subsequently become available. The ensemble of classifiers then is combined through a weighted majority voting procedure. Learn++ is independent of the specific classifier(s) comprising the ensemble, and hence may be used with any supervised learning algorithm. The voting procedure also allows Learn++ to estimate the confidence in its own decision. We present the algorithm and its promising results on two separate ultrasonic weld inspection applications.

Journal Article↗