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Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

Reliable machine learning and statistical analysis rely on diverse, well-distributed training data. However, real-world datasets are often limited in size and exhibit underrepresentation across key subpopulations, leading to biased…

Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…

We introduce a dynamic neural algorithm called Dynamic Neural (DN) SARSA(\lambda) for learning a behavioral sequence from delayed reward. DN-SARSA(\lambda) combines Dynamic Field Theory models of behavioral sequence representation,…

Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…

Probabilistic security assessment and real-time dynamic security assessments (DSA) are promising to better handle the risks of system operations. The current methodologies of security assessments may require many time-domain simulations for…

Real-world applications often require learning continuously from a stream of data under ever-changing conditions. When trying to learn from such non-stationary data, deep neural networks (DNNs) undergo catastrophic forgetting of previously…

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…

Machine learning models are vulnerable to tiny adversarial input perturbations optimized to cause a very large output error. To measure this vulnerability, we need reliable methods that can find such adversarial perturbations. For image…

Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about…

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…

Children possess the ability to learn multiple cognitive tasks sequentially, which is a major challenge toward the long-term goal of artificial general intelligence. Existing continual learning frameworks are usually applicable to Deep…

Neural networks have achieved remarkable performance in computer vision, however they are vulnerable to adversarial examples. Adversarial examples are inputs that have been carefully perturbed to fool classifier networks, while appearing…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…

The optimal design of neural networks is a critical problem in many applications. Here, we investigate how dynamical systems with polynomial nonlinearities can inform the design of neural systems that seek to emulate them. We propose a…

In this paper, we elucidate how representations in deep neural networks (DNNs) evolve during training. Our focus is on overparameterized learning settings where the training continues much after the trained DNN starts to perfectly fit its…