Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “equation learning”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Linear shaped-charge jet optimization using machine learning methods

Linear shaped charges are used to focus energy into rapidly creating a deep linear incision. The general design of a shaped charge involves detonating a confined mass of high explosive (HE) with a metal-lined concave cavity on one side to produce a high velocity jet for the purpose of striking and penetrating a given material target. This jetting effect occurs due to the interaction of the detonation wave with the cavity geometry, which produces an unstable fluid phenomenon known as the Richtmyer–Meshkov instability and results in the rapid growth of a long narrow jet. We apply machine learning and optimization methods to hydrodynamics simulations of linear shaped charges to improve the simulated jet characteristics. The designs that we propose and investigate in this work generally involve modifying the behavior of the detonation waves prior to interaction with the liner material. These designs include the placement of multiple detonators and the use of metal inclusions within the HE. In conclusion, we are able to produce a linear shaped-charge design with a higher penetration depth than the baseline case that we consider and accomplish this using the same amount of or less HE.

36 MATERIALS SCIENCE↗
DOE OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗
NASA NTRSDate not supplied

Physics Informed Neural Nets for Systems Health Management

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Development in data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. The research work presents application of physics-informed neural nets application to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage.

Physics Informed↗
DOE OSTI2023

Crustal Scale Travel Time Prediction with the SALSA3D Framework and Machine Learning

The SALSA3D project aims to improve our models used in travel time prediction. The current version uses tomographic modeling for propagation through the Earth’s mantle because of the large number (order of millions) of observations of seismic phases which primarily traverse the Earth’s mantle and the ability to pose the travel time problem as a set of linear equations. However, all seismic rays traverse the crust to reach receivers at the surface and therefore models of propagation through the crust are required. Therefore, the primary motivation for this study is to explore how to increase the scope of the SALSA3D project to phases which travel primarily through the crust. In this report, we evaluate new, machine learning based and physics-based methods to model these travel times for integration into the SALSA3D framework. Our results suggest that using our existing physics-based travel time tomography method is a viable approach for the regional to global scale, but better predictive capabilities can be achieved through a neural network trained on the region of interest for near-regional offsets. We suggest future iterations of SALSA3D should incorporate machine learning tools such as Physics-Informed Neural Networks or Bayesian Neural Networks.

58 GEOSCIENCES↗
DOE OSTI2024

Data Science Enabled Enabled Discovery of Superconductors (Final Progress Report)

This Final Technical Report describes efforts by 4 PIs at the University of Florida (Peter Hirschfeld, Richard Hennig, Greg Stewart and James Hamlin), over the period September 2019-August 2023, to use data science and machine learning techniques to discover new conventional superconductors. The PIs constructed a discovery loop with two theorists and two experimentalists to: develop algorithms to machine learn descriptors correlating strongly with the critical temperature Tc (PI's Peter Hirschfeld, UF Physics and Richard Hennig, UF Materials Science and En), synthesize and measure properties of promising materials, and feed back the knowledge gained into the prediction algorithm. This work was motivated by the theoretical prediction and experimental discovery of high-pressure, high-pressure hydride superconductors, and to find ways to recreate the high critical temperatures in these systems at ambient pressure. Highlights from the grant include: 1) a new equation for Tc in terms of moments of the electron-phonon spectral function, improving on the so-called Allen-Dynes equation (1975); 2) study of the metastable A15 superconductor Nb3Si, formed under explosive compression at ~1000GPa to determine the kinetic barrier to the ground state structure; 3) the development of ultra-fast machine-learned atomic potentials for molecular dynamics, and 4) the discovery of superconductivity at 19K in WB2 arising from metastable defect structures in the crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Model-based and Model-free Designs for an Extended Continuous-time LQR with Exogenous Inputs

We present an extended linear quadratic regulator (LQR) design for continuous-time linear time-invariant (LTI) systems in the presence of exogenous inputs. We first propose a model-based solution with cost minimization guarantees for states and inputs using dynamic programming (DP). The control law consists of a combination of the optimal state feedback and an additional optimal term dependent on the exogenous inputs. The control gains for the two components are obtained by solving a set of matrix differential equations. We provide these solutions for both finite horizons and steady-state cases. In the second part of the paper, we formulate a reinforcement learning (RL) based algorithm which does not need any model information except the input matrix, and can compute an approximate steady-state LQR gain using measurements of the states, the control inputs, and the exogenous inputs. Both model-based and data-driven optimal control algorithms are tested with a numerical example under different exogenous inputs showcasing the effectiveness of the designs.

Mukherjee, Sayak↗
DOE OSTI2024

Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as—to our knowledge—no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Deep Image Prior Enabled Full Waveform Inversion (Final Technical Report)

MS Student Naveen Gupta worked on the problem of full waveform inversion (FWI) using neural networks as shown in Figure 1. Our goal was to learn a neural network to represent the subsurface velocity model, which when fed into the FWI module (implemented using a numerical forward model of wave equations) produces amplitude estimates that match with ground-truth observations of amplitude. We used neural networks to solve the inverse problem of estimating velocity distributions for a given seismic amplitude data such that, once trained, our neural network model can generate a distribution of velocity profiles for different random vectors fed as inputs to the neural network model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Reducing Operator Complexity of Galerkin Coarse-grid Operators with Machine Learning

Here, we propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in multigrid (MG) methods, addressing the well-known issue of increasing operator complexity. Guided by the MG theory on spectrally equivalent coarse-grid operators, we have developed novel machine learning algorithms that utilize neural networks combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall MG convergence for solving parametric partial differential equation problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and comparison with existing methods for computing non-Galerkin coarse-grid operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Estimating Fault Friction From Seismic Signals in the Laboratory

Nearly all aspects of earthquake rupture are controlled by the friction along the fault that progressively increases with tectonic forcing but in general cannot be directly measured. We show that fault friction can be determined at any time, from the continuous seismic signal. In a classic laboratory experiment of repeating earthquakes, we find that the seismic signal follows a specific pattern with respect to fault friction, allowing us to determine the fault's position within its failure cycle. Using machine learning, we show that instantaneous statistical characteristics of the seismic signal are a fingerprint of the fault zone shear stress and frictional state. Further analysis of this fingerprint leads to a simple equation of state quantitatively relating the seismic signal power and the friction on the fault. Finally, these results show that fault zone frictional characteristics and the state of stress in the surroundings of the fault can be inferred from seismic waves, at least in the laboratory.

58 GEOSCIENCES↗
DOE OSTI2019

Response of a Memristive Biomembrane and Demonstration of Potential Use in Online Learning

The pervasive von Neumann architecture uses complex processor cores and sequential computation. In contrast, the brain is massively parallel and highly efficient, owing to the ability of the neurons and synapses to store and process information simultaneously and to adapt according to incoming information. These features have motivated researchers to develop a host of brain-inspired computers, devices, and models, collectively referred to as neuromorphic computing systems. The quest for synaptic materials capable of closely mimicking biological synapses has led to an alamethicin-doped, synthetic biomembrane with volatile memristive properties which can emulate key synaptic functions to facilitate learning and computation. In contrast to its solid-state counterparts, this two-terminal, biomolecular memristor features similar structure, switching mechanisms, and ionic transport modality as biological synapses while consuming considerably lower power. To use the device as a circuit element, it is important to understand its response to different kinds of input signals. Here we develop a simplified closed form analytical solution based on the underlying state equations for pulse and sine wave inputs. A Verilog-A model based on Runge-Kutta method was developed to incorporate the device in a circuit simulator. Finally, the paper demonstrates possible applications for short- and long-term learning using its unique volatile memristive properties.

Hasan, Md Sakib↗
DOE OSTI2025

Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks

Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.

autoencoder neural networks↗
DOE OSTI2022

Neural-network based collision operators for the Boltzmann equation

Kinetic gas dynamics in rarefied and moderate-density regimes have complex behavior associated with collisional processes. These processes are generally defined by convolution integrals over a high-dimensional space (as in the Boltzmann operator), or require evaluating complex auxiliary variables (as in Rosenbluth potentials in Fokker-Planck operators) that are challenging to implement and computationally expensive to evaluate. In this work, we develop a data-driven neural network model that augments a simple and inexpensive BGK collision operator with a machine-learned correction term, which improves the fidelity of the simple operator with a small overhead to overall runtime. The composite collision operator has a tunable fidelity and, in this work, is trained using and tested against a direct-simulation Monte-Carlo (DSMC) collision operator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Toward data assimilation of ship-induced aerosol–cloud interactions

Satellite imagery can detect temporary cloud trails or ship tracks formed from aerosols emitted from large ships traversing our oceans, a phenomenon that global climate models cannot directly reproduce. Ship tracks are observable examples of marine cloud brightening, a potential solar climate intervention that shows promise in helping combat climate change. In this paper, we demonstrate a simulation-based approach in learning the behavior of ship tracks based upon a novel stochastic emulation mechanism. Our method uses wind fields to determine the movement of aerosol–cloud tracks and uses a stochastic partial differential equation (SPDE) to model their persistence behavior. This SPDE incorporates both a drift and diffusion term which describes the movement of aerosol particles via wind and their diffusivity through the atmosphere, respectively. We first present our proposed approach with examples using simulated wind fields and ship paths. We then successfully demonstrate our tool by applying the approximate Bayesian computation method-sequential Monte Carlo for data assimilation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A systematic comparison of machine learning methods for modeling of dynamic processes applied to combustion emission rate modeling

Ten established, data-driven dynamic algorithms are surveyed and a practical guide for understanding these methods generated. Existing Python programming packages for implementing each algorithm are acknowledged, and the model equations necessary for prediction are presented. A case study on a coal-fired power plant’s NO x emission rates is performed, directly comparing each modeling method’s performance on a mutual system. Each model is evaluated by its root mean squared error (RMSE) on out-of-sample future horizon predictions. Optimal hyperparameters are identified using either an exhaustive search or genetic algorithm. The top five model structures of each method are used to recursively predict future NO x emission rates over a 60-step time horizon. The RMSE at each future timestep is determined, and the recursive output prediction trends compared against measurements in time. The GRU neural network is identified as the best candidate for representing the system, demonstrating accurate and stable predictions across the future horizon by all considered models, while satisfactory performance was observed in several of the ARX/NARX formulations. Finally, these efforts have contributed 1) a concise resource of multiple proven dynamic machine learning methods, 2) a practical guide explaining the use of these methods, effectively lowering the “barrier-to-entry” of deploying such models in control systems, 3) a comparison study evaluating each method’s performance on a mutual system, 4) demonstration of accurate multi-timestep emissions modeling suitable for systems-level control, and 5) generalizable results demonstrating the suitability of each method for prediction over a multi-step future horizon to other complex dynamic systems.

42 ENGINEERING↗
DOE OSTI2023

Physics–Informed Neural Networks of the Saint–Venant Equations for Downscaling a Large–Scale River Model

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical representations of tidal rivers limit the performance of such models at resolving the complex flow dynamics near the river-ocean interface, resulting in inaccurate simulations of flood inundation. In this research, we propose a machine learning (ML) framework based on the state-of-the-art physics-informed neural network (PINN) to simulate the downscaled flow at the subgrid scale. First, we demonstrate that PINN is able to assimilate observations of various types and solve the one-dimensional (1-D) Saint-Venant equations (SVE) directly. We perform the flow simulations over a floodplain and along an open channel in several synthetic case studies. The PINN performance is evaluated against analytical solutions and numerical models. Our results indicate that the PINN solutions of water depth have satisfactory accuracy with limited observations assimilated. In the case of flood wave propagation induced by storm surge and tide, a new neural network architecture is proposed based on Fourier feature embeddings that seamlessly encodes the periodic tidal boundary condition in the PINN's formulation. Furthermore, we show that the PINN-based downscaling can produce more reasonable subgrid solutions of the along-channel water depth by assimilating observational data. The PINN solution outperforms the simple linear interpolation in resolving the topography and dynamic flow regimes at the subgrid scale. This study provides a promising path towards improving emulation capabilities in large-scale models to characterize fine-scale coastal processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Cross Inference of Throughput Profiles Using Micro Kernel Network Method

Dedicated network connections are being increasingly deployed in cloud, centralized and edge computing and data infrastructures, whose throughput profiles are critical indicators of the underlying data transfer performance. Due to the cost and disruptions to physical infrastructures, network emulators, such as Mininet, are often used to generate measurements needed to estimate throughput profiles, typically expressed as a function of the connection round trip time. The profiles estimated using measurements from such emulated networks are usually inaccurate for high bandwidth and high latency connections, since they do not accurately reflect the critical network transport dynamics mainly due to computing and memory constraints of the host. We present a machine learning (ML) method to estimate the throughput profiles using emulation measurements to closely match the testbed and production network profiles. In particular, we propose a micro Kernel Network (mKN) that provides baseline throughput measurements on the host running Mininet emulations, which are used to learn a regression map that converts them to the corresponding testbed measurement estimates. Once initially learned, this map is applied to measurements from subsequent network emulations on the same host. We present experimental measurements to illustrate this approach, and derive generalization equations for the proposed mKN-ML method. Using a four-site scenario emulation, we show the effectiveness of this method in providing accurate concave throughput profiles from inaccurate convex or non-smooth ones indicated by Mininet emulation.

Rao, Nageswara↗