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At least 469 records · Page 26

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. Additionally, we illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

97 MATHEMATICS AND COMPUTING↗

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Latent space dynamics identification for interface tracking with application to shock-induced pore collapse

Capturing sharp, evolving interfaces remains a central challenge in reduced-order modeling, especially when data is limited and the system exhibits localized nonlinearities or discontinuities. Here, we propose LaSDI-IT (Latent Space Dynamics Identification for Interface Tracking), a data-driven framework that combines low-dimensional latent dynamics learning with explicit interface-aware encoding to enable accurate and efficient modeling of physical systems involving moving material boundaries. At the core of LaSDI-IT is a revised autoencoder architecture that jointly reconstructs the physical field and an indicator function representing material regions or phases, allowing the model to track complex interface evolution without requiring detailed physical models or mesh adaptation. The latent dynamics are learned through linear regression in the encoded space and generalized across parameter regimes using Gaussian process interpolation with greedy sampling. We demonstrate LaSDI-IT on the problem of shock-induced pore collapse in high explosives, a process characterized by sharp temperature gradients and dynamically deforming pore geometries. The method achieves relative prediction errors below 9% across the parameter space, accurately recovers key quantities of interest such as pore area and hot spot formation, and matches the performance of dense training with only half the data. This latent dynamics prediction was 10 6 times faster than the conventional high-fidelity simulation, proving its utility for multi-query applications. These results highlight LaSDI-IT as a general, data-efficient framework for modeling discontinuity-rich systems in computational physics, with potential applications in multiphase flows, fracture mechanics, and phase change problems.

Gaussian process↗

Even spheres as joint spectra of matrix models

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

97 MATHEMATICS AND COMPUTING↗

Physics informed machine learning for chemistry tabulation

Modeling of turbulent combustion system requires modeling the underlying chemistry and the turbulent transport. Solving both systems simultaneously is computationally prohibitive. Instead, given the difference in scales at which the two sub-systems evolve, the two sub-systems are typically (re)solved separately. Popular approaches such as the Flamelet Generated Manifolds (FGM) use a two-step strategy where the governing reaction kinetics are pre-computed and mapped to a low-dimensional manifold, characterized by a few reaction progress variables (model reduction) and the manifold is then “looked-up” during the run-time to estimate the high-dimensional system state by the turbulent transport system. While existing works have focused on these two steps independently, in this work we show that joint learning of the progress variables and the look-up model, can yield more accurate results. Here, we build on the base formulation and implementation to include the dynamically generated Thermochemical State Variables (Lower Dimensional Dynamic Source Terms). We discuss the challenges in the implementation of this deep neural network architecture and experimentally demonstrate its superior performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanistic origins of excitonic properties in 2D perovskites: Implications for exciton engineering

As the field of 2D halide perovskites (HPs) matures, state-of-the-art techniques to measure important properties, such as the band gap (E g ) and exciton binding energy (E b ), continue to produce inconsistent values. Here, we tackle this long-standing problem by obtaining direct measurements of E g and E b for 31 unique HP structures. The E b values are lower than in previous literature reports and lower than expected from standard theory that assumes excitons are screened by optical-frequency dielectric constants. These low E b values are shown to be a consequence of unique screening effects, such as superlattice screening and phonon screening. Here, we find a strikingly strong correlation between E b and E g and provide design principles to a priori tune E g and E b to their optimal values. As such, this work offers a blueprint for E g -E b engineering of low-dimensional semiconductors as an even more useful replacement for simply band-gap engineering.

14 SOLAR ENERGY↗

Melting of charge density waves in low dimensions

Charge density waves (CDWs) are collective electronic states that can reshape and melt, even while confined within a rigid atomic crystal. In two dimensions, melting is predicted to be distinct, proceeding through partially ordered nematic and hexatic states that are neither liquid nor crystal. Here, we measure and explain how continuous, hexatic melting of incommensurate CDWs occurs in low-dimensional materials. As a CDW is thermally excited, disorder emerges progressively—initially through smooth elastic deformations that modulate the local wavelength and subsequently via the nucleation of topological defects. Experimentally, we track three hallmark signatures of CDW melting—azimuthal superlattice peak broadening, wavevector contraction, and integrated intensity decay.

42 ENGINEERING↗

Development and assessment of hierarchical multi-reward reinforcement learning based potential for silicene with state-of-the-art models

We develop a new interatomic force field for Silicene, a 2D material with a buckled hexagonal lattice structure with high polymorphism. We introduce new parameterizations of a Tersoff model using a hierarchical multi-reward reinforcement learning (RL) methodology coupled with a continuous Monte Carlo Tree Search optimization. Our model significantly outperforms existing methods by enhancing the accuracy of predictions for the structural and thermodynamic properties of seven silicene polymorphs-including structure, energy, equation of state, elasticity, and phonon dispersion-when compared to established models. We further make a comprehensive comparison of the various models in predicting the mechanical and thermal properties of silicene. We trace the origin of the improved performance to the description of the angular dependence in the bond-order term, suggesting that modifying the angular terms in short-range models is essential to capture the structural diversity in low dimensional systems.

2D materials↗

A short account of thermoelectric film characterization techniques

Thermoelectric films and periodic structures have particularly intriguing electrical and thermal transport features due to their low dimensionality. As a result, they have piqued the attention of researchers from across the spectrum of disciplines. Their applications span from cooling fast CPUs to providing energy for wearable devices. The progress in the techniques for synthesizing TE materials and fabricating thin films has facilitated the emergence of a flourishing research domain in the field of electrical and thermal transport at the nanoscale. Further, a significant proportion of contemporary electronic, opto-electronic, and solar energy components are composed of materials featuring numerous interfaces and nanoscale contacts. Consequently, it is imperative to explore the thermal energy transfer and charge carrier transport across the films with thickness dimensions in the nanometer range. The development of cutting-edge approaches for grasping complicated processes at the nanoscale is critical. This review provides a concise overview of the prevalent methodologies developed over the last two decades and employed for the characterization of the Seebeck coefficient and electrical and thermal conductivity of thermoelectric films.

36 MATERIALS SCIENCE↗

Hybrid printing of wearable piezoelectric sensors

Piezoelectricity provides an ideal electromechanical mechanism with emerging applications in wearable devices due to its simplicity and self-powered nature. However, the 3D printing of piezoelectric devices still faces many challenges, including material printability, high energy poling process, and low dimensional accuracy. This study demonstrates, for the first time, a tellurium nanowire-based piezoelectric device fabricated by a hybrid printing method integrating highly complementary aerosol jet printing and extrusion printing in a single printing platform. The aerosol-jet-printed tellurium nanowire demonstrates piezoelectric properties without the need for any poling processing due to the unique properties of the tellurium nanowires. The silver nanowire electrodes printed by aerosol jet printing demonstrate excellent conductivity and stretchability without the need for sintering. An extrusion method is employed to print the silicone films, which serve as the stretchable substrate and the electrical insulation layers between the printed tellurium and silver. The printed wearable piezoelectric devices were attached to a human wrist to detect different hand gestures and to a human neck to detect heartbeat without using an external power source. In conclusion, the fully printed, sintering-free and poling-free, and stretchable piezoelectric device opens enormous opportunities for facile integration with a broad range of printed electronics and wearable devices.

47 OTHER INSTRUMENTATION↗

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

97 MATHEMATICS AND COMPUTING↗

Spin excitations and dynamics in 2D magnets: An overview of magnons and magnetic skyrmions

van der Waals magnetic materials open up exciting possibilities to investigate fundamental spin properties in low-dimensional systems and to build compact functional spintronic structures. This review focuses on the recent progress in two-dimensional (2D) magnets that explore beyond the homogenous magnetically ordered state, including magnons (spin waves), magnetic skyrmions, and complex magnetic domains. Properties of these spin and topology excitations in 2D magnets provide insights into spin-orbit interactions and other forms of coupling between electrons, phonons, and spin-dependent excitations. Such spin-based quasiparticles can also serve as information carriers for next-generation high-speed computing elements. Furthermore, we will first lay out the general theoretical basis of dynamical responses in magnetic systems, followed by detailed descriptions of experimental progress in magnons and spin textures (including magnetic domains and skyrmions). Discussion on the experimental techniques and future perspectives are also included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improving the short-wave infrared response of strained GeSn/Ge multiple quantum wells by rapid thermal annealing

In this work, the evolution of structural, optical and optoelectronic properties of coherently strained Ge 0.883 Sn 0.117 /Ge multiple quantum wells (MQWs) grown by molecular beam epitaxy under rapid thermal annealing (RTA) is systematically investigated. The MQW structure remains fully-strained state with RTA at 400 °C or below and disrupts at higher annealing temperatures due to Sn segregation and interdiffusion of Ge and Sn atoms. The GeSn well layers exhibit the strongest absorption in 2.0–2.4 μm after annealing at 400 °C and become transparent above 1.8 μm after RTA at 600 °C or beyond due to serve Sn segregation. Owing to improved crystal quality after RTA at 400 °C, the dark current of the fabricated metal-semiconductor-metal photodetector is effectively lowered by more than two times. Additionally, the responsivities at 1.55 and 2.0 μm are improved by 4.15 and 3.78 folds, respectively, compared to those of the as-grown sample. Here, the results can be an insightful guidance for the development of high-performance short-wave infrared photonic devices based on Sn-containing group-IV low-dimensional structures.

36 MATERIALS SCIENCE↗

Data-driven model for divertor plasma detachment prediction

We present a fast and accurate data-driven surrogate model for divertor plasma detachment prediction leveraging the latent feature space concept in machine learning research. Our approach involves constructing and training two neural networks: an autoencoder that finds a proper latent space representation (LSR) of plasma state by compressing the multi-modal diagnostic measurements and a forward model using multi-layer perception (MLP) that projects a set of plasma control parameters to its corresponding LSR. By combining the forward model and the decoder network from autoencoder, this new data-driven surrogate model is able to predict a consistent set of diagnostic measurements based on a few plasma control parameters. In order to ensure that the crucial detachment physics is correctly captured, highly efficient 1D UEDGE model is used to generate training and validation data in this study. The benchmark between the data-driven surrogate model and UEDGE simulations shows that our surrogate model is capable of providing accurate detachment prediction (usually within a few per cent relative error margin) but with at least four orders of magnitude speed-up, indicating that performance-wise, it has the potential to facilitate integrated tokamak design and plasma control. Comparing with the widely used two-point model and/or two-point model formatting, the new data-driven model features additional detachment front prediction and can be easily extended to incorporate richer physics. This study demonstrates that the complicated divertor and scrape-off-layer plasma state has a low-dimensional representation in latent space. Understanding plasma dynamics in latent space and utilising this knowledge could open a new path for plasma control in magnetic fusion energy research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hole Trapping in Halide Perovskites Induces Phase Segregation

Metal halide perovskites have garnered a great deal of attention for their applications in photovoltaics, LEDs, and radiation detection. The ease of solution processing high-quality perovskite semiconductors with large absorption coefficients and tolerance to native defects is decidedly attractive. Additionally, the ability to precisely tune the band gap of halide perovskites through compositional alloying of the halide ion is of particular interest for a range of applications, especially for tandem solar cells. However, under steady state light irradiation, an initially homogeneous mixed halide perovskite (MHP) will form local domains that are rich in one halide ion (e.g., Br or I). This light-induced phase segregation in MHPs forms iodide-rich domains that act as charge carrier traps and lowers the efficiency of perovskite-based devices. Thus, phase segregation poses a serious challenge to the implementation of MHPs in real-world device settings. Interestingly, when a phase segregated MHP film is placed in the dark, entropic driving forces become dominant and the segregated perovskite remixes and returns to its initially homogeneous state. Several key mechanistic details of phase segregation have been elucidated over the years. However, there are still aspects of halide segregation that are not clear, and there is ongoing debate in the literature as to what are the key factors that contribute to the mechanism. This Account discusses recent results that point to the specific role of hole trapping in phase segregation. Interestingly, generation of holes through above-band-gap excitation or through electrochemical injection increases ion migration and leads to phase segregation. The thermodynamic and redox properties of halide perovskites provide a strong driving force for hole trapping and oxidation of iodide species in MHPs. However, mobile halide species within the perovskite lattice take time to migrate and generate halide-rich domains. When in contact with a nonpolar solvent, the migration of iodine species is further extended to expulsion of iodine from the perovskite film. Thus, the mobility of halides and their susceptibility to hole-induced oxidation play a crucial role in determining the long-term stability of metal halide perovskites. Strategies to gain kinetic control over ion migration to slow phase segregation are needed to overcome these hurdles and achieve stable mixed halide perovskites. Modification of the perovskite composition through introduction of different cations or halide ions, or introduction of low-dimensional perovskite phases may suppress phase segregation. Furthermore, in achieving stability and improving the efficiency of perovskite solar cells and light emitting devices with minimal impacts, suppression of segregation remains the key factor.

36 MATERIALS SCIENCE↗

Structure−Property Relationships in a Series of Hybrid Halopyridinium Ruthenium(IV) Halides

Reported is the synthesis and characterization of a family of hybrid ruthenium halides consisting of haloruthenium octahedra (X = Cl, Br) charge balanced with halopyridinium (XPy; X= H, Cl, Br, I) organic cations which assemble via noncovalent interactions between ion pairs. Diffuse reflectance spectroscopy showed that compounds containing RuBr 6 2- octahedra displayed a lower bandgap (1.05 eV< x < 1.08 eV) compared to compounds with RuCl 6 2- octahedra (1.22 eV < x < 1.43 eV). Additionally, computational density functional theory (DFT) based natural bonding orbital (NBO) analysis and density of state (DOS) methods were used to characterize second-sphere non-covalent interaction strengths and elucidate molecular orbital perturbations to elucidate their influence on Ru-X orbital constructs and in turn rationalize band gap trends. Analyses showed ligand to metal charge transfer is responsible for the small bandgap energies and are unperturbed by second-sphere interactions. Here, this report serves as a platform for probing the relationship between the structural and photophysical properties within the haloruthenium family of low dimensional transition metal halide perovskites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗