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DOE OSTI2025

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗

NASA NTRS1992

Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Kao, Hsiao C.↗

NASA NTRS2007

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

Farassat, F.↗

DOE OSTI2021

Bayesian optimization for chemical products and functional materials

The design of chemical-based products and functional materials is vital to modern technologies, yet remains expensive and slow. Artificial intelligence and machine learning offer new approaches to leverage data to overcome these challenges. Herein this review focuses on recent applications of Bayesian optimization (BO) to chemical products and materials including molecular design, drug discovery, molecular modeling, electrolyte design, and additive manufacturing. Numerous examples show how BO often requires an order of magnitude fewer experiments than Edisonian search. The essential equations for BO are introduced in a self-contained primer specifically written for chemical engineers and others new to the area. Finally, the review discusses four current research directions for BO and their relevance to product and materials design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Quantifying uncertainties and correlations in the nuclear-matter equation of state

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory (χ EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χ EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. Furthermore, we then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium χ EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

Here in this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various DNN architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equation, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a nonintrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly nonintrusive since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate and can be used as a robust predictive tool for nonintrusive model order reduction of complex fluid flows.

42 ENGINEERING↗

DOE OSTI2021

Machine learning to alleviate Hubbard-model sign problems

Lattice Monte Carlo calculations of interacting systems on nonbipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times, the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. Furthermore, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper, we demonstrate that neural networks can be trained to parametrize suitable manifolds for this class of sign problem and drastically reduce the computational cost for different severely afflicted small volume systems. In particular, we apply our method to the Hubbard model on the triangle and tetrahedron, both of which are nonbipartite. At strong interaction strengths and modest temperatures, the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Evaluating the causes of cost reduction in photovoltaic modules

Photovoltaic (PV) module costs have declined rapidly over forty years but the reasons remain elusive. Here we advance a conceptual framework and quantitative method for quantifying the causes of cost changes in a technology, and apply it to PV modules. Our method begins with a cost model that breaks down cost into variables that changed over time. Cost change equations are then derived to quantify each variable's contribution. We distinguish between changes observed in variables of the cost model – which we term low-level mechanisms of cost reduction – and research and development, learning-by-doing, and scale economies, which we refer to as high-level mechanisms. We find that increased module efficiency was the leading low-level cause of cost reduction in 1980–2012, contributing almost 25% of the decline. Government-funded and private R&D was the most important high-level mechanism over this period. After 2001, however, scale economies became a more significant cause of cost reduction, approaching R&D in importance. Policies that stimulate market growth have played a key role in enabling PV's cost reduction, through privately-funded R&D and scale economies, and to a lesser extent learning-by-doing. The method presented here can be adapted to retrospectively or prospectively study many technologies, and performance metrics besides cost.

14 SOLAR ENERGY↗

DOE OSTI2017

Machine learnt bond order potential to model metal–organic (Co–C) heterostructures

A fundamental understanding of the inter-relationships between structure, morphology, atomic scale dynamics, chemistry, and physical properties of mixed metallic-covalent systems is essential to design novel functional materials for applications in flexible nano-electronics, energy storage and catalysis. To achieve such knowledge, it is imperative to develop robust and computationally efficient atomistic models that describe atomic interactions accurately within a single framework. Here, we present a unified Tersoff–Brenner type bond order potential (BOP) for a Co–C system, trained against lattice parameters, cohesive energies, equation of state, and elastic constants of different crystalline phases of cobalt as well as orthorhombic Co2C derived from density functional theory (DFT) calculations. The independent BOP parameters are determined using a combination of supervised machine learning (genetic algorithms) and local minimization via the simplex method. Our newly developed BOP accurately describes the structural, thermodynamic, mechanical, and surface properties of both the elemental components as well as the carbide phases, in excellent accordance with DFT calculations and experiments. Using our machine-learnt BOP potential, we performed large-scale molecular dynamics simulations to investigate the effect of metal/carbon concentration on the structure and mechanical properties of porous architectures obtained via self-assembly of cobalt nanoparticles and fullerene molecules. Such porous structures have implications in flexible electronics, where materials with high electrical conductivity and low elastic stiffness are desired. Using unsupervised machine learning (clustering), we identify the pore structure, pore-distribution, and metallic conduction pathways in self-assembled structures at different C/Co ratios. We find that as the C/Co ratio increases, the connectivity between the Co nanoparticles becomes limited, likely resulting in low electrical conductivity; on the other hand, such C-rich hybrid structures are highly flexible (i.e., low stiffness). The BOP model developed in this work is a valuable tool to investigate atomic scale processes, structure–property relationships, and temperature/pressure response of Co–C systems, as well as design organic–inorganic hybrid structures with a desired set of properties.

Narayanan, Badri↗

DOE OSTI2026

Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems

Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.

Holstein model↗

DOE OSTI2024

Probabilistic measures for biological adaptation and resilience

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Deep Electric Field Predictions by Drift-Reduced Braginskii Theory with Plasma-Neutral Interactions Based on Experimental Images of Boundary Turbulence

We present 2-dimensional turbulent electric field calculations via physics-informed deep learning consistent with (i) drift-reduced Braginskii theory under the framework of an axisymmetric fusion plasma with purely toroidal field and (ii) experimental estimates of the fluctuating electron density and temperature on open field lines obtained from analysis of gas puff imaging of a discharge on the Alcator C-Mod tokamak. The inclusion of effects from the locally puffed atomic helium on particle and energy sources within the reduced plasma turbulence model are found to strengthen correlations between the electric field and electron pressure. The neutrals are also directly associated with broadening the distribution of turbulent field amplitudes and increasing ${\bf E \times B}$ shearing rates. As a result, this demonstrates a novel approach in plasma experiments by solving for nonlinear dynamics consistent with partial differential equations and data without encoding explicit boundary nor initial conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2007

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗

DOE OSTI2023

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

58 GEOSCIENCES↗

DOE OSTI2025

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

DOE OSTI2019

Subtask 1.1 – Advanced Characterization of Unconventional Oil and Gas Reservoirs to Enhance CO2 Storage Resource Estimates

The Energy & Environmental Research Center (EERC) developed methods and approaches for advanced characterization of unconventional oil and gas reservoirs to enhance CO2 storage resource estimates using samples collected from organic-rich shales of the Bakken Formation. The project was funded under U.S. Department of Energy (DOE) Cooperative Agreement No. DE-FE0024233, with nonfederal cost share provided by Hitachi High Technologies America. The project participants included the EERC, Hitachi High Technologies America, the team at the National Energy Technology Laboratory’s (NETL’s) computed tomography (CT) scanning laboratory in Morgantown, West Virginia, and several NETL staff who have worked on CO2 storage resource estimation. Investigations on the use of subsurface geologic formations for CO2 storage have been ongoing for many years. In the last decade, improvements in directional drilling technology and hydraulic fracturing of organic-rich shale and other tight rock formations have opened new opportunities for CO2 storage, with the potential cobenefit of enhancing gas and oil recovery. Gas-bearing, organic-rich shales have been of particular interest as a carbon storage target because their ability to store large volumes of CO2 is implied by their ability to store methane; however, estimating the CO2 storage resource of organic-rich shales and other unconventional reservoirs is challenging because of the lack of detailed geologic and petrophysical data that are needed to develop improved volumetric equations. According to NETL’s method for estimating regional-scale CO2 storage resources, the key factors that control CO2 storage in geologic formations include void space within induced fractures, natural fractures and matrix pores, as well as the occurrence and distribution of organic matter (OM) and clay minerals. A key goal of this effort was to use field emission scanning electron microscopy (FESEM) analysis of fine-grain unconventional reservoir rocks coupled with advanced image analysis and machine learning techniques to quantify the occurrence and distribution of porosity, OM, and clay minerals. By better understanding the potential migration pathways of CO2 within tight rocks and quantifying the occurrence of sorptive components (OM and clays) along potential flow pathways, methods to estimate the CO2 storage resource of such rocks can be refined. The Bakken petroleum system (Bakken) was used as the source of rock samples for this effort because it includes organic-rich shales with contrasting degrees of thermal maturity as well as tight, nonshale clastic rocks with varying clay mineral content. To better understand the key components of interest in tight rock samples, the EERC worked closely with Hitachi to optimize the FESEM settings necessary to resolve the sample mineralogy, porosity and OM content at micro- to nanoscale resolution. The EERC also worked closely with Hitachi to apply and improve its advanced mineral identification and characterization system (AMICS) software so that it is better suited for mineral identification at the high resolution necessary to resolve features of interest in fine-grained rocks such as organic-rich shales. The EERC also applied advanced image analysis software packages, including Ilastik, to classify and quantify the key components of interest within the samples using FESEM imagery. These advanced techniques allowed for quantification and differentiation of the void space within fractures, pores and OM, as well as a technique to determine and quantify the key mineral and OM components surrounding pore spaces. Being able to better quantify the void space and the potential accessibility of CO2 to sorptive minerals or OM within tight rocks allows for improved estimation of the CO2 storage resource potential of organic-rich shales and other unconventional formations. The information derived from the image analysis techniques was used to refine NETL’s method for estimating regional-scale CO2 storage resources in collaboration with staff from NETL. An additional goal of this work was to better understand rates of CO2 permeation, flow pathways, and sorption in organic-rich shales and nonshale reservoir rocks and to evaluate potential changes in CO2 flow over time. The EERC conducted long-duration (several weeks) CO2 flow-through testing at reservoir conditions using Bakken shale and nonshale samples to assess CO2 permeation rates and retention/sorption within core plugs to represent bulk matrix behavior. Conventional isothermal adsorption testing over a range of pressure conditions was also performed on pulverized Bakken samples to better assess potential maximum sorptive capacity of the samples. The results of this testing illustrated the higher sorptive capacity of the Bakken shales when compared to the sorptive capacity of the nonshale reservoir rock, which contains very little OM when compared to the Bakken shales. The results also illustrate the differences in permeation behavior as a function of fracture flow versus matrix flow. In an attempt to visualize CO2 permeation and flow behavior in Bakken shale samples over time, the EERC collaborated with NETL’s CT Lab in Morgantown, West Virginia. A variety of tests were performed at the NETL lab on unfractured and fractured samples of the Bakken shale. The unfractured Bakken shale samples did not result in CO2 migration within the samples over the testing duration; thus imagery of CO2 migration pathways within the matrix of Bakken samples was not obtained. The results of the flow-through testing within fractured samples illustrate changes in CO2 permeation rates over time, with a trend of decreasing CO2 flow over time. The results of this effort suggest that FESEM analysis coupled with advanced image analysis and machine learning techniques are effective in characterizing and quantifying the mineralogy, porosity, fractures, and OM content of 2-D imagery at the high resolution needed to identify features of interest in tight rocks. In addition, the image analysis techniques allow for identification and quantification of different porosity types as well as the key mineral components and/or OM that CO2 would contact in the reservoir as it migrates through pores and fracture networks. This is key information needed to better estimate the CO2 storage resource potential of organic-rich shales and other tight reservoirs. Additional work is needed to determine the sorptive capacity of the individual sample components (OM and clay minerals) at reservoir conditions so that this approach and the refined CO2 storage resource equation can be applied to other shale and unconventional reservoirs. In addition, subsequent work should be performed to better understand the number of images needed to use stereological approaches to estimate the volume of sample components using 2-D imagery, to explore machine learning techniques to differentiate between induced vs. natural fractures, and to estimate the connectivity of pores and fracture networks using 2-D imagery. Being able to derive this information at the microscale would facilitate scaling up of the sample characterization data used for reservoir modeling and simulation to estimate the CO2 storage resource potential of tight formations.

03 NATURAL GAS↗

DOE OSTI2025

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗

DOE OSTI2020

Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Abstract Radiation‐induced photocurrent in semiconductor devices can be simulated using complex physics‐based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high‐level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large‐scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced‐order discrete‐time dynamical systems from time series data based on singular value decomposition. To obtain physics‐aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced‐order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density—which can be used to calculate the induced current at the device boundaries—while remaining compact enough to incorporate into larger circuit simulations.

Hanson, Joshua↗