Related papers: Machine Learning for Complex Systems Dynamics: Det…

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

Early-exiting dynamic neural networks (EDNN), as one type of dynamic neural networks, has been widely studied recently. A typical EDNN has multiple prediction heads at different layers of the network backbone. During inference, the model…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…

Drought stress is a major threat to global crop productivity, making its early and precise detection essential for sustainable agricultural management. Traditional approaches, though useful, are often time-consuming and labor-intensive,…

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system…

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…

Deep Neural Networks (DNN) have found numerous applications in various domains, including fraud detection, medical diagnosis, facial recognition, and autonomous driving. However, DNN-based systems often suffer from reliability issues due to…

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…

Time series anomaly detection plays a critical role in automated monitoring systems. Most previous deep learning efforts related to time series anomaly detection were based on recurrent neural networks (RNN). In this paper, we propose a…

Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a…

Fault diagnostics and prognostics are important topics both in practice and research. There is an intense pressure on industrial plants to continue reducing unscheduled downtime, performance degradation, and safety hazards, which requires…

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…

System identification under unknown external excitation is an inherently ill-posed problem, typically requiring additional knowledge or simplifying assumptions to enable reliable state and parameter estimation. The difficulty of the problem…

The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting…

Deep neural networks (DNNs) are notoriously hard to understand and difficult to defend. Extracting representative paths (including the neuron activation values and the connections between neurons) from DNNs using software engineering…

Imagine experiencing a crash as the passenger of an autonomous vehicle. Wouldn't you want to know why it happened? Current end-to-end optimizable deep neural networks (DNNs) in 3D detection, multi-object tracking, and motion forecasting…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Understanding the behaviour of environmental extreme events is crucial for evaluating economic losses, assessing risks, health care and many other aspects. In the spatial context, relevant for environmental events, the dependence structure…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…