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At least 37 records · Page 2

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

Abstract Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.

97 MATHEMATICS AND COMPUTING↗

Data assimilation in operator algebras

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

A seamless multiscale operator neural network for inferring bubble dynamics

Modelling multiscale systems from nanoscale to macroscale requires the use of atomistic and continuum methods and, correspondingly, different computer codes. Here, we develop a seamless method based on DeepONet, which is a composite deep neural network (a branch and a trunk network) for regressing operators. In particular, we consider bubble growth dynamics, and we model tiny bubbles of initial size from 100 nm to 10 $\mathrm {\mu }\textrm {m}$ , modelled by the Rayleigh–Plesset equation in the continuum regime above 1 $\mathrm {\mu }\textrm {m}$ and the dissipative particle dynamics method for bubbles below 1 $\mathrm {\mu }\textrm {m}$ in the atomistic regime. After an offline training based on data from both regimes, DeepONet can make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. The framework of DeepONet is general and can be used for unifying physical models of different scales in diverse multiscale applications.

Mechanics↗

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗

In Situ Infrared Spectroscopy of a Plasma Jet and Data-Driven Solution of Multi-Scale Plasma Chemistry Problems

Multi-scale problems are commonly known in many scientific and engineering fields where microscopic behaviors are coupled with macroscopic processes. This is also an unsolved problem in low-temperature plasma chemistry where hundreds of chemical species are involved in thousands of chemical reactions. To address this problem, a physics-informed data-driven modeling is developed to solve such a multi-scale problem using the experimental Fourier-transform infrared spectroscopy (FTIR) measurements of several species’ concentrations. The modeling based on modern machine learning techniques provides concentrations of other relevant species along with the electron temperature and gas temperature at the location of FTIR measurements. For example, the concentrations O, OH, and H 2 O 2 play key roles in plasma-based cancer therapy. This approach overcomes the multi-scale difficulties of microscopic low-temperature plasma chemistry coupling with macroscopic gas flow and allows the acquisition of a full picture of output species concentrations. Presented here for the helium-air jet at atmospheric pressure, the ML-based modeling can be used to describe and possibly control multiscale systems using partial experimental data sets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Supervised pixel classification using a feature space derived from an artificial visual system

Image segmentation involves labelling pixels according to their membership in image regions. This requires the understanding of what a region is. Using supervised pixel classification, the paper investigates how groups of pixels labelled manually according to perceived image semantics map onto the feature space created by an Artificial Visual System. Multiscale structure of regions are investigated and it is shown that pixels form clusters based on their geometric roles in the image intensity function, not by image semantics. A tentative abstract definition of a 'region' is proposed based on this behavior.

Baxter, Lisa C.↗

Thermal Conductivity of 3D Woven Composite Thermal Protection System Materials via Multiscale Recursive Micromechanics

Multiscale micromechanics predictions have been made for the effective thermal conductivities and local thermal fields for a novel 3D woven composite thermal protection system material. The Multiscale Recursive Micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses a recently developed version of the High-Fidelity Generalized Method of Cells micromechanics theory at each of three length scales. Results focus on the impact of the microstructural geometry representation at each length scale on the material’s effective thermal conductivity, along with the local thermal flux and temperature fields induced in the microstructures.

Composites↗

Thermal Conductivity of 3D Woven Composite Thermal Protection System Materials via Multiscale Recursive Micromechanics

Multiscale micromechanics predictions have been made for the effective thermal conductivities and local thermal fields for a novel 3D woven composite thermal protection system material. The Multiscale Recursive Micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses a recently developed version of the High-Fidelity Generalized Method of Cells micromechanics theory at each of three length scales. Results focus on the impact of the microstructural geometry representation at each length scale on the material’s effective thermal conductivity, along with the local thermal flux and temperature fields induced in the microstructures.

composite↗

2040 Vision: A Roadmap for Integrated, Multiscale Materials and System Modeling and Simulation

Over the last few decades, advances in high-performance computing, new materials characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) and additive manufacturing have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. While these advances have driven significant progress in the development of aerospace components and systems, that progress has been limited by persistent technology and infrastructure challenges that must be overcome to realize the full potential of integrated materials and systems design and simulation modeling throughout the supply chain. As a result, NASA's Transformational Tools and Technology (TTT) Project sponsored a study (performed by a team led by Pratt & Whitney) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This talk will describe the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); associated critical gaps and actions to close those gaps; and major recommendations). This roadmap is a community consensus document and is a result of over 450 professionals input obtain via: i) four society workshops (AIAA, NAFEMS, and two TMS), ii) community-wide survey, and iii) the establishment of 9 expert panels (one per key element) consisting on average 10 non-team members from academia, government and industry to review, update content, and prioritize gaps and actions. It is NASA's hope and desire that this roadmap provides the strategic guidance to both public and private research and development decision makers to make the proposed 2040 vision state a reality and thereby provide a significant advancement in the United States global competitiveness.

Multiscale Modeling↗

Beyond Price-Taker: Multiscale Optimization of Wind and Battery Integrated Energy Systems

Integrating renewable energy into the electric grid is challenging due to the intermittency and variability of wind and other non-dispatchable resources. Integrated energy systems (IESs) combine multiple energy technologies (e.g., fossil, nuclear, renewables, storage) to reduce costs and improve flexibility and reliability. However, standard techno-economic analysis (TEA) methods often overestimate the benefits of IESs because they fail to account for energy market adjustments. This paper systematically studies the limitations of the prevailing price-taker assumption for TEA and optimization of hybrid energy systems. As an illustrative case study, we retrofit an existing wind farm in the RTS-GMLC test system (which loosely mimics the Southwest U.S.) with battery energy storage to form an IES. We show that the standard price-taker model overestimates the electricity revenue and the net present value (NPV) of the IES up to 178% and 30.4%, respectively, compared to our more rigorous multiscale optimization. These differences arise because introducing storage creates a more flexible resource that impacts the larger wholesale electricity market. Moreover, this work highlights the impact of the IES has on the market via various strategic bidding, and underscores the importance of moving beyond price-taker for optimal storage sizing and TEA of IESs. We conclude by discussing opportunities to generalize the proposed framework to other IESs, and highlight emerging research questions regarding the complex interactions between IESs and markets.

25 ENERGY STORAGE↗

Advances in imaging, scattering, spectroscopy, and machine learning-aided approaches for multiscale characterization of cementitious systems

Recent progress in methods used in the multiscale characterization of cementitious systems is reviewed, focusing on advances in imaging, scattering, and spectroscopy. The review includes relevant applications and developments in machine learning and other data analytics approaches to enhance characterization. Developments in imaging using light and electron microscopy as well as x-ray (i.e., from synchrotron) methods are summarized. Updates include scanning electron microscopy (SEM), transmission electron microscopy (TEM), tomography, and holography. A critical overview of spectroscopy (e.g., MAS NMR, Raman) and scattering (e.g., neutron, x-ray, synchrotron x-ray) methods is provided, and the intersection of these with imaging is developed (e.g., Raman imaging). Additionally, the paper summarizes recent developments in and implementations of state-of-the-art machine-learning algorithms and data analytics methods for automated, systematic, and/or quantitative analyses of image data sets. The review considers but is not limited to the application of these methods for investigating the hydration and microstructure development of cement phases, low-carbon-footprint cements (e.g., limestone calcined clay cements, LC3), environmental interactions (e.g., ASR) and model systems. Finally, the present work provides a critical presentation of advances in characterization methods that link together the composition and multiscale structure of cementitious materials.

42 ENGINEERING↗

Emergent Recursive Multiscale Interaction in Complex Systems

This project studied the potential for multiscale group dynamics in complex social systems, including emergent recursive interaction. Current social theory on group formation and interaction focuses on a single scale (individuals forming groups) and is largely qualitative in its explanation of mechanisms. We combined theory, modeling, and data analysis to find evidence that these multiscale phenomena exist, and to investigate their potential consequences and develop predictive capabilities. In this report, we discuss the results of data analysis showing that some group dynamics theory holds at multiple scales. We introduce a new theory on communicative vibration that uses social network dynamics to predict group life cycle events. We discuss a model of behavioral responses to the COVID-19 pandemic that incorporates influence and social pressures. Finally, we discuss a set of modeling techniques that can be used to simulate multiscale group phenomena.

42 ENGINEERING↗

Dynamic coevolution of baseflow and multiscale groundwater flow system during prolonged droughts

Field and numerical studies suggest that baseflow is composed of waters from a spectrum of groundwater flow paths termed the Groundwater Flow System (GWFS) – from shallow hillslope contributions to watershed-scale deep circulation originating in headwaters and discharging into lowland rivers. Here, we explore the evolution of the GWFS under prolonged droughts to understand its dynamics and multiscale nature, and to elucidate its role in baseflow generation and recession at the watershed scale. In this work, we consider three drought scenarios of varying severity and simulate groundwater flow in a 2-D cross-section of an idealized watershed with deep permeable bedrock, tracking the evolution of flow paths, baseflow, and residence times during the recession process. We find that baseflow generation at different drainage stages, and within different subwatersheds, is influenced distinctly by flow paths of different scales, depending on the relative strength of the flow paths and the position of the subwatersheds relative to the recharge/discharge zones of the deeper watershed-scale groundwater circulation. Despite having the same local relief, geology, and climate, baseflow from each subwatershed has a distinct recession behavior and time-dependent residence time distribution. Also, the hydraulic and transport characteristics of baseflow generation co-evolve and are strongly affected by the connection state of the water table to subwatersheds. These findings suggest that asynchrony and dissimilarity of baseflow generation from hillslopes under the impact of the watershed-scale groundwater flow, and interactions with local-scale and intermediate-scale groundwater flow, must be taken into account when interpreting baseflow recession data and building conceptual baseflow models at the watershed scale.

54 ENVIRONMENTAL SCIENCES↗

Magnetospheric Multiscale Instrument Suite Operations and Data System

The four Magnetospheric Multiscale (MMS) spacecraft will collect a combined volume of approximately 100 gigabits per day of particle and field data. On average, only 4 gigabits of that volume can be transmitted to the ground. To maximize the scientific value of each transmitted data segment, MMS has developed the Science Operations Center (SOC) to manage science operations, instrument operations, and selection, downlink, distribution, and archiving of MMS science data sets. The SOC is managed by the Laboratory for Atmospheric and Space Physics (LASP) in Boulder, Colorado and serves as the primary point of contact for community participation in the mission. MMS instrument teams conduct their operations through the SOC, and utilize the SOC's Science Data Center (SOC) for data management and distribution. The SOC provides a single mission data archive for the housekeeping and science data, calibration data, ephemerides, attitude and other ancillary data needed to support the scientific use and interpretation. All levels of data products will reside at and be publicly disseminated from the SDC. Documentation and metadata describing data products, algorithms, instrument calibrations, validation, and data quality will be provided. Arguably, the most important innovation developed by the SOC is the MMS burst data management and selection system. With nested automation and 'Scientist-in-the-Loop' (SITL) processes, these systems are designed to maximize the value of the burst data by prioritizing the data segments selected for transmission to the ground. This paper describes the MMS science operations approach, processes and data systems, including the burst system and the SITL concept.

Baker, D. N.↗

MATEY: multiscale adaptive transformer models for spatiotemporal physical systems

Accurate representation of the multiscale features in spatiotemporal physical systems using vision transformer architectures requires extremely long, computationally prohibitive token sequences. To address this issue, we propose two novel adaptive tokenization schemes that dynamically adjust patch sizes based on local features: one ensures convergent behavior to uniform patch refinement, while the other offers better computational efficiency. Moreover, we present a set of spatiotemporal attention schemes, where the temporal or axial spatial dimensions are decoupled, to evaluate their baseline computational and data efficiencies and to determine whether adaptive tokenization can improve this performance. We assess the performance of the proposed multiscale adaptive model, MATEY, in a sequence of experiments. Compared to a full spatiotemporal attention scheme or a scheme that decouples only the temporal dimension, we find that fully decoupled axial attention is less efficient and expressive, requiring more training time and model parameters to achieve the same accuracy. The experiments on the adaptive tokenization schemes show that, compared to a uniformly refined model, the proposed schemes achieve comparable or improved accuracy at a much lower cost in the tested two-dimensional settings. While the asymptotic analysis suggests the potential for favorable scaling, empirical validation at substantially longer sequence lengths remains to be performed in future work. Finally, we demonstrate in two fine-tuning tasks featuring different physics that models pretrained on PDEBench data outperform the ones trained from scratch, especially in the low data regime with frozen attention.

adaptive tokenization↗