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At least 829 records · Page 46

Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.

Corbetta, Matteo↗

Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, {PIML} models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, {PIML} models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of {PIML} is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in {PIML} for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of {PIML} models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Nghiem, Truong↗

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗

Unique contributions of chlorophyll and nitrogen to predict crop photosynthetic capacity from leaf spectroscopy

The photosynthetic capacity or the CO 2 -saturated photosynthetic rate (Vmax), chlorophyll, and nitrogen are closely linked leaf traits that determine C 4 crop photosynthesis and yield. Accurate, timely, rapid, and non-destructive approaches to predict leaf photosynthetic traits from hyperspectral reflectance are urgently needed for high-throughput crop monitoring to ensure food and bioenergy security. Therefore, this study thoroughly evaluated the state-of-the-art physically based radiative transfer models (RTMs), data-driven partial least squares regression (PLSR), and generalized PLSR (gPLSR) models to estimate leaf traits from leaf-clip hyperspectral reflectance, which was collected from maize (Zea mays L.) bioenergy plots with diverse genotypes, growth stages, treatments with nitrogen fertilizers, and ozone stresses in three growing seasons. The results show that leaf RTMs considering bidirectional effects can give accurate estimates of chlorophyll content (Pearson correlation r=0.95), while gPLSR enabled retrieval of leaf nitrogen concentration (r=0.85). Using PLSR with field measurements for training, the cross-validation indicates that V max can be well predicted from spectra (r=0.81). Here, the integration of chlorophyll content (strongly related to visible spectra) and nitrogen concentration (linked to shortwave infrared signals) can provide better predictions of V max (r=0.71) than only using either chlorophyll or nitrogen individually. This study highlights that leaf chlorophyll content and nitrogen concentration have key and unique contributions to V max prediction.

59 BASIC BIOLOGICAL SCIENCES↗

Data from Unique Contributions of Chlorophyll and Nitrogen to Predict Crop Photosynthetic Capacity from Leaf Spectroscopy

The photosynthetic capacity or the CO2-saturated photosynthetic rate (Vmax), chlorophyll, and nitrogen are closely linked leaf traits that determine C4 crop photosynthesis and yield. Accurate, timely, rapid, and non-destructive approaches to predict leaf photosynthetic traits from hyperspectral reflectance are urgently needed for high-throughput crop monitoring to ensure food and bioenergy security. Therefore, this study thoroughly evaluated the state-of-the-art physically based radiative transfer models (RTMs), data-driven partial least squares regression (PLSR), and generalized PLSR (gPLSR) models to estimate leaf traits from leaf-clip hyperspectral reflectance, which was collected from maize (Zea mays L.) bioenergy plots with diverse genotypes, growth stages, treatments with nitrogen fertilizers, and ozone stresses in three growing seasons. The results show that leaf RTMs considering bidirectional effects can give accurate estimates of chlorophyll content (Pearson correlation r=0.95), while gPLSR enabled retrieval of leaf nitrogen concentration (r=0.85). Using PLSR with field measurements for training, the cross-validation indicates that Vmax can be well predicted from spectra (r=0.81). The integration of chlorophyll content (strongly related to visible spectra) and nitrogen concentration (linked to shortwave infrared signals) can provide better predictions of Vmax (r=0.71) than only using either chlorophyll or nitrogen individually. This study highlights that leaf chlorophyll content and nitrogen concentration have key and unique contributions to Vmax prediction.

Biomass Analytics↗

Regime shifts in Arctic terrestrial hydrology manifested from impacts of climate warming

Abstract. Anthropogenic warming in the Arctic is causing hydrological cycle intensification and permafrost thaw, with implications for flows of water, carbon, and energy from terrestrial biomes to coastal zones. To better understand the likely impacts of these changes, we used a hydrology model driven by meteorological data from atmospheric reanalysis and two global climate models for the period 1980–2100. The hydrology model accounts for soil freeze–thaw processes and was applied across the pan-Arctic drainage basin. The simulations point to greater changes over northernmost areas of the basin underlain by permafrost and to the western Arctic. An acceleration of simulated river discharge over the recent past is commensurate with trends drawn from observations and reported in other studies. Between early-century (2000–2019) and late-century (2080–2099) periods, the model simulations indicate an increase in annual total runoff of 17 %–25 %, while the proportion of runoff emanating from subsurface pathways is projected to increase by 13 %–30 %, with the largest changes noted in summer and autumn and across areas with permafrost. Most notably, runoff contributions to river discharge shift to northern parts of the Arctic Basin that contain greater amounts of soil carbon. Each season sees an increase in subsurface runoff; spring is the only season where surface runoff dominates the rise in total runoff, and summer experiences a decline in total runoff despite an increase in the subsurface component. The greater changes that are seen in areas where permafrost exists support the notion that increased soil thaw is shifting hydrological contributions to more subsurface flow. The manifestations of warming, hydrological cycle intensification, and permafrost thaw will impact Arctic terrestrial and coastal environments through altered river flows and the materials they transport.

54 ENVIRONMENTAL SCIENCES↗

Data-Driven Global Sensitivity Analysis of Three-Phase Distribution System with PVs

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV variations plays an important role in designing optimal voltage control schemes. This paper proposes a Kriging, i.e., Gaussian process modeling enabled data-driven GSA method. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol index can be conveniently calculated to assess the global sensitivity of voltage to various power injection variations. Comparison results with other model-based GSA methods on the IEEE 37-bus feeder, such as the polynomial chaos expansion and the Monte Carlo approaches demonstrate that the proposed method can achieve accurate GSA outcomes while maintaining high computational efficiency.

distribution system analysis↗

Learning continuous models for continuous physics

Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

97 MATHEMATICS AND COMPUTING↗

Using Co-Optimized Machine Learned Manifolds for Modeling Chemically Reacting Flows

Chemically reacting flows play a key role in a wide range of engineered systems, from chemical and polymer processing to combustion-based energy conversion technologies. Simulations of these flows involve solving a coupled set of partial differential equations for mass, momentum, energy, and all relevant chemical species in the system. Chemical reaction pathways may be extremely complex and involve hundreds or more intermediate species, with reactions that occur over timescales varying by several orders of magnitude - presenting a significant numerical stiffness challenge. The combination of these factors makes simulation of chemically reacting flows vastly more expensive than nonreactive simulations, and often makes direct solution of the governing equations intractable. It is necessary to apply lower-fidelity models in place of the detailed governing equations in order to reduce computational cost to enable reacting flow simulation tools to be used in the engineering design process. Many of the models employed for this purpose are based on reducing the dimension of the thermochemical state, motivated by the observation that the observed thermochemical states in a system lie on a low-dimensional manifold in thermochemical state space. This behavior occurs due to the fast equilibration of certain reactive and transport processes, and physics-based manifold models rely on idealized assumptions about the balance of timescales and the way in which chemistry and transport are coupled. In this work, we apply a novel method for data-driven manifold-based modeling that can leverage data from high-fidelity reacting flow simulations to improve model accuracy in cases where the physics-based modeling assumptions break down. The approach is designed to be broadly applicable across chemically reacting flow systems but is applied here to turbulent combustion modeling.

machine learning↗

Data-Driven Approach to Transactive Energy Systems with Commercial Buildings

A microgrid with solar, storage, and responsive load resources has been implemented and tested on an urban academic campus. Through modeling and simulation, a consensus transactive energy mechanism has been implemented, with each resource participating as a virtual battery. Most owners of large buildings don't have the information and expertise to develop and validate suitable models of their buildings using available tools. To mitigate this adoption barrier, a data-driven building model has been implemented and validated. It uses 5-minute weather data, 3-second revenue meter data, energy audit information, and a load reduction test conducted by the building owner.

Buildings, data-driven modeling, deep learning, en↗

Graph-based Compact Modeling (GCM) of CMOS transistors for efficient parameter extraction: A machine learning approach

Parameter extraction of compact transistor models is an expensive process, heavily relying on engineering knowledge and experience. To automate such a process, we propose a novel approach, Graph-based Compact Model (GCM), that integrates physical modeling and data-driven learning. GCM utilizes Graph Neural Networks (GNNs) to establish the model structure, while retaining the physicality in compact models. Here, we implement our GCM in Verilog-A to support circuit simulations. As demonstrated with an academic 7 nm FinFET PDK, the new approach automatically generates a GCM model within a minute, and achieves excellent accuracy and efficiency in SPICE.

42 ENGINEERING↗

Reduced‐Order Modeling for Linearized Representations of Microphysical Process Rates

Abstract Representing cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical variables used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data‐driven reduced‐order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions. Using simulations characteristic of marine stratiform clouds, we simultaneously learn lower dimensional representations of droplet size distributions and predict the evolution of the microphysical state of the system. Droplet collision‐coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of three. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision‐coalescence in models. We demonstrate how deep learning based reduced‐order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision‐coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment‐based representations.

54 ENVIRONMENTAL SCIENCES↗

Accelerating kinetic plasma simulations with machine-learning-generated initial conditions

Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Artificial neural networks↗

Prognostics for Systems Health Management - Model and Hybrid Based Approaches. Where are We Heading?

To facilitate and solve the prediction problem, awareness of the current state and health of the system is key, since it is necessary to perform condition-based system health predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditional. In case of next generation electric aircrafts, computing remaining flying time is safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. In order to tackle and solve the prediction problem, it is essential to have awareness of the current health state of the system, especially since it is necessary to perform condition-based predictions. To be able to predict the future state of the system, it is also required to possess knowledge of the current and future operational conditions and flight profiles for accurate estimation of end-of-discharge (EOD) for the batteries. Similar framework can be implemented to other complex systems and subsystems. Our research approach is to develop a system level health monitoring safety indicator which runs estimation and prediction algorithms to estimate remaining useful life predictions at system, subsystem swell as component levels. Given models of the current and future system behavior, a general approach of model-based prognostics is discussed as a solution to the prediction problem and further for decision making. Data driven prognostics approaches have been equally used with good results in the past, where respective approaches have their own challenges to tackle. This limits their applicability to complex real-world domains: (a) high complexity or incompleteness of physics-based models and (b) limited representativeness of the training dataset for data-driven models. With the advent of internet of things for data collection and increased use of ML algorithms, hybrid approaches are the next avenue to reduce the challenges and achieve better results. An hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, we use physics-based performance models to infer unobservable model parameters related to the system's components health solving a calibration problem.

Prognostics↗

Reliable modeling and prediction of precipitation & radiation for mountainous hydrology

This White Paper focuses on data-driven atmospheric process model emulation and atmospheric process surrogate model development. It proposes leveraging recent AI advances in these approaches to fill in unavoidable observational gaps and enable high-fidelity modeling/predictability of the atmosphere and land-surface interactions in mountainous watersheds. This approach will support studies and predictability of water cycle extremes.

54 ENVIRONMENTAL SCIENCES↗