1,563 research outputs found
An Expert's Guide to Training Physics-informed Neural Networks
Physics-informed neural networks (PINNs) have been popularized as a deep
learning framework that can seamlessly synthesize observational data and
partial differential equation (PDE) constraints. Their practical effectiveness
however can be hampered by training pathologies, but also oftentimes by poor
choices made by users who lack deep learning expertise. In this paper we
present a series of best practices that can significantly improve the training
efficiency and overall accuracy of PINNs. We also put forth a series of
challenging benchmark problems that highlight some of the most prominent
difficulties in training PINNs, and present comprehensive and fully
reproducible ablation studies that demonstrate how different architecture
choices and training strategies affect the test accuracy of the resulting
models. We show that the methods and guiding principles put forth in this study
lead to state-of-the-art results and provide strong baselines that future
studies should use for comparison purposes. To this end, we also release a
highly optimized library in JAX that can be used to reproduce all results
reported in this paper, enable future research studies, as well as facilitate
easy adaptation to new use-case scenarios.Comment: 36 pages, 25 figures, 13 table
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
Adaptive non linear system identification and channel equalization usinf functional link artificial neural network
In system theory, characterization and identification are fundamental problems. When the plant behavior is completely unknown, it may be characterized using certain model and then, its identification may be carried out with some artificial neural networks(ANN) like multilayer perceptron(MLP) or functional link artificial neural network(FLANN) using some learning rules such as back propagation (BP) algorithm. They offer flexibility, adaptability and versatility, so that a variety of approaches may be used to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. The primary aim of the present thesis is to provide a framework for the systematic design of adaptation laws for nonlinear system identification and channel equalization. While constructing an artificial neural network the designer is often faced with the problem of choosing a network of the right size for the task. The advantages of using a smaller neural network are cheaper cost of computation and better generalization ability. However, a network which is too small may never solve the problem, while a larger network may even have the advantage of a faster learning rate. Thus it makes sense to start with a large network and then reduce its size. For this reason a Genetic Algorithm (GA) based pruning strategy is reported. GA is based upon the process of natural selection and does not require error gradient statistics. As a consequence, a GA is able to find a global error minimum. Transmission bandwidth is one of the most precious resources in digital communication systems. Communication channels are usually modeled as band-limited linear finite impulse response (FIR) filters with low pass frequency response. When the amplitude and the envelope delay response are not constant within the bandwidth of the filter, the channel distorts the transmitted signal causing intersymbol interference (ISI). The addition of noise during propagation also degrades the quality of the received signal. All the signal processing methods used at the receiver's end to compensate the introduced channel distortion and recover the transmitted symbols are referred as channel equalization techniques.When the nonlinearity associated with the system or the channel is more the number of branches in FLANN increases even some cases give poor performance. To decrease the number of branches and increase the performance a two stage FLANN called cascaded FLANN (CFLANN) is proposed.This thesis presents a comprehensive study covering artificial neural network (ANN) implementation for nonlinear system identification and channel equalization. Three ANN structures, MLP, FLANN, CFLANN and their conventional gradient-descent training methods are extensively studied. Simulation results demonstrate that FLANN and CFLANN methods are directly applicable for a large class of nonlinear control systems and communication problems
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