We introduce a method to successively locate equilibria (steady states) of dynamical systems on Riemannian manifolds. The manifolds need not be characterized by an a priori known atlas or by the zeros of a smooth map. Instead, they can be defined by point-clouds and sampled as needed through an iterative process. If the manifold is an Euclidean space, our method follows isoclines, curves along which the direction of the vector field $X$ is constant. For a generic vector field $X$, isoclines are smooth curves and every equilibrium lies on isoclines. We generalize the definition of isoclines to Riemannian manifolds through the use of parallel transport: generalized isoclines are curves along which the directions of $X$ are parallel transports of each other. As in the Euclidean case, generalized isoclines of generic vector fields $X$ are smooth curves that connect equilibria of $X$. Our algorithm can be regarded as an extension of the method of Newton trajectories to the manifold setting when the manifold is unknown. This work is motivated by computational statistical mechanics, specifically high dimensional (stochastic) differential equations that model the dynamics of molecular systems. Often, these dynamics concentrate near low-dimensional manifolds and have transitions (saddle points with a single unstable direction) between metastable equilibria. We employ iteratively sampled data and isoclines to locate these saddle points. Coupling a black-box sampling scheme (e.g., Markov chain Monte Carlo) with manifold learning techniques (diffusion maps in the case presented here), we show that our method reliably locates equilibria of $X$.

Neural ordinary differential equations (Neural ODEs) define continuous time dynamical systems with neural networks. The interest in their application for modelling has sparked recently, spanning hybrid system identification problems and time series analysis. In this work we propose the use of a neural control policy capable of satisfying state and control constraints to solve nonlinear optimal control problems. The control policy optimization is posed as a Neural ODE problem to efficiently exploit the availability of a dynamical system model. We showcase the efficacy of this type of deterministic neural policies in two constrained systems: the controlled Van der Pol system and a bioreactor control problem. This approach represents a practical approximation to the intractable closed-loop solution of nonlinear control problems.

Electrical faults may trigger blackouts or wildfires without timely monitoring and control strategy. Traditional solutions for locating faults in distribution systems are not real-time when network observability is low, while novel black-box machine learning methods are vulnerable to stochastic environments. We propose a novel Physics-Preserved Graph Network (PPGN) architecture to accurately locate faults at the node level with limited observability and labeled training data. PPGN has a unique two-stage graph neural network architecture. The first stage learns the graph embedding to represent the entire network using a few measured nodes. The second stage finds relations between the labeled and unlabeled data samples to further improve the location accuracy. We explain the benefits of the two-stage graph configuration through a random walk equivalence. We numerically validate the proposed method in the IEEE 123-node and 37-node test feeders, demonstrating the superior performance over three baseline classifiers when labeled training data is limited, and loads and topology are allowed to vary.

Hansen Technologies, a leading global provider of software and services to the energy, water and communications industries, is pleased to announce that it has signed a multi-year agreement with the City of New Bern, part of the State of North Carolina, as the city charts a new digital transformation journey and envisions a new technological infrastructure. Under the terms of the agreement, Hansen will provide Hansen CIS, part of the Hansen Suite for Energy and Utilities, to the historical city, delivered through a SaaS (Software as a Service) model – marking another successful progression in Hansen's Cloud and SaaS-based CIS strategy within North America. This continues to meet the evolving needs of North American utilities and municipalities as they look to migrate towards more flexible and scalable software platforms. This will modernize New Bern's existing infrastructure and enable the replacement of their existing systems. Equipped with enhanced UI configuration capabilities and an expanded integration framework, Hansen CIS empowers utilities and municipalities to manage the full customer service and revenue lifecycle for water and energy-related services.

Components of Robots were not used in literature until Karel Capek's play "Rossum's Universal Robots" in 1921. The first motion picture to include a robot that looked like a human was "Metropolis" in 1926. Robots are now a common sight in our daily lives. Components of Robots now work in our warehouses and manufacturing facilities; explore far-off planets; assist us in inspecting our infrastructure sites, and even help us build entirely new ones. But how do robots truly function?

Aspiring bakers are frequently called upon to adapt award-winning recipes based on differing kitchen setups. Someone might use an eggbeater instead of a stand mixer to make prize-winning chocolate chip cookies, for instance. Being able to reproduce a recipe in different situations and with varying setups is critical for both talented chefs and computational scientists, the latter of whom are faced with a similar problem of adapting and reproducing their own "recipes" when trying to validate and work with new AI models. These models have applications in scientific fields ranging from climate analysis to brain research. "When we talk about data, we have a practical understanding of the digital assets we deal with," said Eliu Huerta, scientist and lead for Translational AI at the U.S. Department of Energy's (DOE) Argonne National Laboratory.

We propose a clustering procedure to group K populations into subgroups with the same dependence structure. The method is adapted to paired population and can be used with panel data. It relies on the differences between orthogonal projection coefficients of the K density copulas estimated from the K populations. Each cluster is then constituted by populations having significantly similar dependence structures. A recent test statistic from Ngounou-Bakam and Pommeret (2022) is used to construct automatically such clusters. The procedure is data driven and depends on the asymptotic level of the test. We illustrate our clustering algorithm via numerical studies and through two real datasets: a panel of financial datasets and insurance dataset of losses and allocated loss adjustment expense.

Ferromagnetic shape memory alloys (MSMAs), such as Ni-Mn-Ga single crystals, can exhibit the shape memory effect due to an applied magnetic field at room temperature. Under a variable magnetic field and a constant bias stress loading, MSMAs have been used for actuation applications. This work introduced a new feature to the existing macroscale magneto-mechanical model for Ni-Mn-Ga single crystal. This model includes the fact that the magnetic easy axis in the two variants is not exactly perpendicular as observed by D silva et al. This offset helps explain some of the power harvesting capabilities of MSMAs. Model predictions are compared to experimental data collected on a Ni-Mn-Ga single crystal. The experiments include both stress-controlled loading with constant bias magnetic field load (which mimics power harvesting or sensing) and fieldcontrolled loading with constant bias compressive stress (which mimics actuation). Each type of test was performed at several different load levels, and the applied field was measured without the MSMA specimen present so that demagnetization does not affect the experimentally measured field as suggested by Eberle et al. Results show decent agreement between model predictions and experimental data. Although the model predicts experimental results decently, it does not capture all the features of the experimental data. In order to capture all the experimental features, finally, a generalized regression neural network (GRNN) was used to train the experimental data (stress, strain, magnetic field, and emf) so that it can make a reasonably better prediction.

Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent predictions, which makes them unreliable in practice. In this paper, we leverage the framework of Irreversible port-Hamiltonian Systems (IPHS), which can describe most multi-physics systems, and rely on Neural Ordinary Differential Equations (NODEs) to learn their parameters from data. Since IPHS models are consistent with the first and second principles of thermodynamics by design, so are the proposed Physically Consistent NODEs (PC-NODEs). Furthermore, the NODE training procedure allows us to seamlessly incorporate prior knowledge of the system properties in the learned dynamics. We demonstrate the effectiveness of the proposed method by learning the thermodynamics of a building from the real-world measurements and the dynamics of a simulated gas-piston system. Thanks to the modularity and flexibility of the IPHS framework, PC-NODEs can be extended to learn physically consistent models of multi-physics distributed systems.

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. We draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as \emph{multilevel-in-width} to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully-connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.