Related papers: Dynamical Mechanism of Sampling-based Stochastic I…

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then…

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with…

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical…

There has long been debates on how we could interpret neural networks and understand the decisions our models make. Specifically, why deep neural networks tend to be error-prone when dealing with samples that output low softmax scores. We…

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…

Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…

Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…

Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant…

A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are…

Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Urban environments pose a significant challenge for autonomous vehicles (AVs) as they must safely navigate while in close proximity to many pedestrians. It is crucial for the AV to correctly understand and predict the future trajectories of…

While deep neural networks take loose inspiration from neuroscience, it is an open question how seriously to take the analogies between artificial deep networks and biological neuronal systems. Interestingly, recent work has shown that deep…

Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…