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At least 775 records · Page 43

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Charging infrastructure access and operation to reduce the grid impacts of deep electric vehicle adoption

Electric vehicles will contribute to emissions reductions in the United States, but their charging may challenge electricity grid operations. We present a data-driven, realistic model of charging demand that captures the diverse charging behaviours of future adopters in the US Western Interconnection. We study charging control and infrastructure build-out as critical factors shaping charging load and evaluate grid impact under rapid electric vehicle adoption with a detailed economic dispatch model of 2035 generation. We find that peak net electricity demand increases by up to 25% with forecast adoption and by 50% in a stress test with full electrification. Locally optimized controls and high home charging can strain the grid. Shifting instead to uncontrolled, daytime charging can reduce storage requirements, excess non-fossil fuel generation, ramping and emissions. Our results urge policymakers to reflect generation-level impacts in utility rates and deploy charging infrastructure that promotes a shift from home to daytime charging.

33 ADVANCED PROPULSION SYSTEMS↗

Effects of oxidation and impurities in lithium surfaces on the emitting wall plasma sheath

The use of lithium as a surface coating in fusion devices improves the plasma performance, but the change in the wall properties affects the secondary electron emission properties of the material. Lithium oxidizes easily, which drives the emission yield well above unity. We present here simulations demonstrating the change in the sheath structure from monotonic to the nonmonotonic space-charge limited sheath using an energy-dependent data-driven emission model, which self-consistently captures both secondary emission and backscattering populations. Increased secondary electron emission from the material has ramifications for the degradation and erosion of the wall. The results show that the oxidation leads to an increased electron energy flux into the wall and a reduced ion energy flux. The net transfer of energy to the surface is significantly greater for the oxidized case than for the pure lithium case. High backscattering rates of low-energy particles lead to a high re-emission rate at the wall.

Fusion reactors↗

A broad-host-range event detector: expanding and quantifying performance between Escherichia coli and Pseudomonas species

Modern microbial biodesign relies on the principle that well-characterized genetic parts can be reused and reconfigured for different functions. However, this paradigm has only been successful in a limited set of hosts, mostly comprised from common lab strains of Escherichia coli . It is clear that new applications such as chemical sensing and event logging in complex environments will benefit from new host chassis. This study quantitatively compared how the same chemical event logger performed across four strains and three different microbial species. An integrase-based sensor and memory device was operated by two representative soil Pseudomonads— Pseudomonas fluorescens SBW25 and Pseudomonas putida DSM 291. Quantitative comparisons were made between these two non-traditional hosts and two benchmark E. coli chassis including the probiotic Nissle 1917 and common cloning strain DH5α. The performance of sensor and memory components changed according to each host, such that a clear chassis effect was observed and quantified. These results were obtained via fluorescence from reporter proteins that were transcriptionally fused to the integrase and downstream recombinant region and via data-driven kinetic models. The Pseudomonads proved to be acceptable chassis for the operation of this event logger, which outperformed the common E. coli DH5α in many ways. This study advances an emerging frontier in synthetic biology that aims to build broad-host-range devices and understand the context by which different species can execute programmable genetic operations.

59 BASIC BIOLOGICAL SCIENCES↗

AI & Physics-Based Bad Command/Data Detection in Large Power Electronics Systems: Multi-Port Autonomous Reconfigurable Solar Power Plant (MARS)

Detection of bad data from measurement sensors and bad commands from control centers need to be carried out to avoid instabilities within large power electronics systems. Towards the same, in this paper, model and data driven methods are proposed to identify anomalies in measured data and commands received by large power electronics systems. The large power electronics system considered in this paper is a multi-port autonomous reconfigurable solar power plant (MARS), which consists of photovoltaic (PV) and energy storage systems (ESSs) that connect to high-voltage direct current (HVdc) system and transmission ac power grid. The proposed algorithms in the MARS power plant to detect bad data from measurements and bad commands from control centers are evaluated in simulations and hardware-in-the-loop (HIL) tests. Furthermore, it has been observed that the proposed algorithms are able to detect bad measurements and commands in all the use cases evaluated.

14 SOLAR ENERGY↗

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

A population data-driven workflow for COVID-19 modeling and learning

CityCOVID is a detailed agent-based model that represents the behaviors and social interactions of 2.7 million residents of Chicago as they move between and colocate in 1.2 million distinct places, including households, schools, workplaces, and hospitals, as determined by individual hourly activity schedules and dynamic behaviors such as isolating because of symptom onset. Disease progression dynamics incorporated within each agent track transitions between possible COVID-19 disease states, based on heterogeneous agent attributes, exposure through colocation, and effects of protective behaviors of individuals on viral transmissibility. Throughout the COVID-19 epidemic, CityCOVID model outputs have been provided to city, county, and state stakeholders in response to evolving decision-making priorities, while incorporating emerging information on SARS-CoV-2 epidemiology. Here we demonstrate our efforts in integrating our high-performance epidemiological simulation model with large-scale machine learning to develop a generalizable, flexible, and performant analytical platform for planning and crisis response.

97 MATHEMATICS AND COMPUTING↗

Unstructured clinical notes within the 24 hours since admission predict short, mid & long-term mortality in adult ICU patients

Mortality prediction for intensive care unit (ICU) patients is crucial for improving outcomes and efficient utilization of resources. Accessibility of electronic health records (EHR) has enabled data-driven predictive modeling using machine learning. However, very few studies rely solely on unstructured clinical notes from the EHR for mortality prediction. In this work, we propose a framework to predict short, mid, and long-term mortality in adult ICU patients using unstructured clinical notes from the MIMIC III database, natural language processing (NLP), and machine learning (ML) models. Depending on the statistical description of the patients’ length of stay, we define the short-term as 48-hour and 4-day period, the mid-term as 7-day and 10-day period, and the long-term as 15-day and 30-day period after admission. We found that by only using clinical notes within the 24 hours of admission, our framework can achieve a high area under the receiver operating characteristics (AU-ROC) score for short, mid and long-term mortality prediction tasks. The test AU-ROC scores are 0.87, 0.83, 0.83, 0.82, 0.82, and 0.82 for 48-hour, 4-day, 7-day, 10-day, 15-day, and 30-day period mortality prediction, respectively. We also provide a comparative study among three types of feature extraction techniques from NLP: frequency-based technique, fixed embedding-based technique, and dynamic embedding-based technique. Lastly, we provide an interpretation of the NLP-based predictive models using feature-importance scores.

60 APPLIED LIFE SCIENCES↗

Predicting initial trans-membrane pressure across cycles in the ultrafiltration process using random forest

With growing freshwater scarcity, direct potable reuse (DPR) systems that reclaim wastewater for drinking are becoming increasingly important for sustainable water supply. Reliable operation requires minimizing downtime in ultrafiltration (UF) units, where membrane fouling leads to elevated trans-membrane pressure (TMP). This study develops data-driven regression models based on random forest (RF) and autoregressive (AR) approaches to forecast the initial TMP at the start of each UF filtration cycle in a pilot-scale DPR system. The RF model consistently outperforms baseline methods, including historical mean, last observation carried forward, and AR models, across multiple forecast horizons, achieving the lowest root mean square error. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent input variables across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is assessed for both direct and recursive RF modelling approaches. The proposed RF framework establishes a robust foundation for predictive monitoring and real-time optimization of UF operations, supporting sustainable and reliable water reuse.

direct potable reuse↗

AI for Extreme Volcanic Climate Forcing and Feedback Forecasting in the 21st century

Our paradigm-shifting framework will apply machine learning and perform physical analysis of contemporary volcanoes to develop sound forecasts of extreme eruptions in the 21stcentury and their abrupt drying and cooling impacts on the warming climate. We will also bridge climate data driven regression models and earth system model output to trace teleconnections that exacerbate regional impacts such as Arctic amplification and western US droughts.

54 ENVIRONMENTAL SCIENCES↗

AI for Extreme Volcanic Climate Forcing and Feedback Forecasting in the 21st century

Focal Areas: Our paradigm-shifting framework will apply machine learning and perform physical analysis of contemporary volcanoes to develop sound forecasts of extreme eruptions in the 21st century and their abrupt drying and cooling impacts on the warming climate. We will also bridge climate data driven regression models and earth system model output to trace teleconnections that exacerbate regional impacts such as Arctic amplification and western US droughts.

54 ENVIRONMENTAL SCIENCES↗