Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or microfluidic networks. In this work, we investigate lattice growth using a two-dimensional, zero-temperature stochastic model of short-range spin interactions. Our goal is to determine how external perturbations can be optimized to steer the system efficiently toward the uniformly positive state, starting from two initial clusters of positive sites. To achieve this, we cast the problem as a Markov decision process adapted for a two-dimensional Ising model with zero-temperature dynamics. Within this framework, we compare alternative growth geometries and identify the structure of optimal strategies across three representative regimes.
Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs projects the high-dimensional full-order model (FOM) dynamics onto a low-dimensional manifold. These projection-based ROMs approaches often rely on classical model reduction techniques such as proper orthogonal decomposition (POD) or, more recently, on neural network architectures such as autoencoders (AEs). In the case that the ROM is constructed by the POD, one has approximation guaranteed based on the singular values of the problem at hand. However, POD-based techniques can suffer from slow decay of the singular values in transport-and advection-dominated problems. In contrast to that, AEs allow for better reduction capabilities than the POD, often with the first few modes, but at the price of theoretical considerations. In addition, it is often observed, that AEs exhibits a plateau of the projection error with the increment of the dimension of the trial manifold. In this work, we propose a deep invertible AE architecture, named inv-AE, that computationally improves upon the stagnation of the reconstruction error typical of traditional AE architectures, e.g., convolutional, and the reconstructions quality. Inv-AE is composed of several invertible neural network layers that allows for gradually recovering more information about the FOM solutions the more we increase the dimension of the reduced manifold. Through the application of inv-AE to a parametric 1dimensional Burgers' equation, a parametric 2-dimensional fluid flow around an obstacle with variable geometry, and a parametric 3-dimensional Korteweg-de Vries, we show that (i) inv-AE mitigates the issue of the characteristic plateau of (convolutional and fully connected) AEs and (ii) inv-AE can be combined with popular autoencoder-based ROM approaches, e.g., DL-ROM and POD-DL-ROM, to improve their accuracy.
We study switching among multiple square selections of output functions (melds) drawn from a deck of candidate outputs for nonlinear systems that are static feedback linearizable via outputs. Fixing an operating point, each meld induces a distinct feedback-linearizing coordinate chart defined on a common neighborhood. Switching between melds therefore produces state-dependent coordinate mismatches that are not represented explicitly in standard fixed-coordinate dwell-time formulations. We quantify this effect through Lipschitz bounds on the cross-chart maps over a compact safe set and introduce a reference-compatibility constant that measures mismatch among reference families across melds. We derive an explicit dwell-time condition depending on the controller decay rates, the reference-compatibility constant, and a bound on the desired-jet resets. The resulting condition guarantees exponential decay of the active-output tracking errors between switches, conditional seamless tracking of shared outputs whose desired jets do not reset, and uniform boundedness of the state error within the safe set. Safe-set invariance follows under an explicit margin condition. A planar 3R manipulator illustrates the results.
“Fairness-aware” algorithms are increasingly used to allocate grid capacity in electrical power systems, yet they often overlook existing disparities between household groups, such as those arising from unequal rooftop solar adoption. Through simulations on a stylized low-voltage grid using electricity data from the Netherlands, we apply demographic parity, a group fairness metric, to compare differences in grid access and costs between households with and without rooftop solar. Three objectives are analyzed: minimal intervention, proportional fairness, and min-max fairness. The results indicate that (1) “fairness-aware” allocation does not eliminate group disparities, (2) voltage violations influence the distribution of burdens and benefits, (3) lower curtailment compensation can reduce disparities between households, and (4) common fairness evaluation metrics do not capture these group disparities. This study advances the discussion on fairness in power systems computation by encouraging further research on how to avoid reinforcing existing disparities.
Wind-speed records are concentrated in common operating ranges, leaving relatively few observations at the low and high ends of the distribution. This study proposes a Rarity-Aware Multi-Scale Gated Echo State Network (RMG-ESN) that combines three reservoir time scales, GRU-inspired state gating, and rarity-weighted readout fitting. Model selection uses three-fold expanding-window time-series cross-validation. Final performance is then evaluated on a 90-day offshore block divided into 18 non-overlapping five-day windows and a 28-day onshore block divided into 28 non-overlapping 24-hour windows. With the reservoir architecture held fixed, rarity weight ing increases offshore QR from 61.54% to 69.26% and reduces RMSE from 1.6658 to 1.2282; onshore QR increases from 68.50% to 78.58% and RMSE decreases from 0.7072 to 0.5235. In the benchmark comparison, CNN-LSTM-Attention has the lowest offshore RMSE, MAE, and MAPE, while RMG-ESN has the highest QR. Onshore, the two models have nearly identical mean RMSE; RMG-ESN has the higher QR, whereas the attention model has the lower MAE and MAPE. Percentile-stratified results vary by wind-speed band, but the controlled ablation shows the same direction of benefit from rarity weighting on both datasets.
