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A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. Furthermore, this improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computer-aided design of stability enhanced nicotinamide cofactor biomimetics for cell-free biocatalysis

Cell-free biocatalysis (CFB) is an efficient and environmentally friendly method to synthesize molecules such as pharmaceuticals, biochemicals, and biofuels through the in vitro use of enzyme cascades. These enzymes often require redox cofactors to drive chemical reactions. Natural redox cofactors (NAD(P)H) are expensive to isolate, motivating synthetic nicotinamide cofactor biomimetics (NCBs) as a cost-effective solution. A select handful of NCBs have been identified as potential NAD(P)H alternatives with comparable or improved redox capabilities, however, they display a tendency to degrade in common buffers. In this study, a library of 132 NCB candidates is systematically generated, over 85% of which have not been characterized in the literature, to expand the diversity of currently explored NCBs. The decomposition mechanism of NCBs in phosphate is evaluated using density functional theory (DFT), revealing protonation at the nicotinamide C5 position as a reporter of cofactor stability. Based on this result, we trained a linear regression model on DFT calculated descriptors to predict NCB stability in phosphate buffer, achieving mean absolute error (MAE) and root mean squared error (RMSE) values within computational accuracy. Analysis of key atomic descriptors and qualitative trends in our dataset informed the design of novel NCB candidates we propose with optimized stability. This work enables researchers to predict the relative stability of NCBs before synthesis, thereby streamlining the process to make CFB more affordable and viable at industry scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Hybrid-Learning Algorithm for Online Dynamic State Estimation in Multimachine Power Systems

With the increasing penetration of distributed generators in the smart grids, having knowledge of rapid real-time electromechanical dynamic states has become crucial to system stability control. Conventional Supervisory Control and Data Acquisition (SCADA)-based dynamic state estimation (DSE) techniques are limited by the slow sampling rates, while the emerging phasor measurement units (PMUs) technology enables rapid real-time measurements at network nodes. Using generator bus terminal voltages, we propose a hybrid-learning DSE (HL-DSE) algorithm to estimate the synchronous machine rotor angle and speed in real time. The HL-DSE takes the power system model into account and trains neuroestimators with real-time data in an online manner. Compared with traditional DSE methods, the HL-DSE overcomes limitations by using a data-driven approach in conjunction with the physical power system model. The time efficiency, accuracy, convergence, and robustness of the proposed algorithm are tested under noises and fault conditions in both small- and large-scale test systems. Simulation results show that the proposed HL-DSE is much more computationally efficient than widely used Kalman filter (KF)-based methods while maintaining comparable accuracy and robustness. In particular, HL-DSE is over 100 times faster than square-root unscented KF (SR-UKF) and 80 times faster than extended KF (EKF). The advantages and challenges of the HL-DSE are also discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

QRF4P-NRT: Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates Using Quantile Regression Forests

Accurate and reliable near-real-time satellite precipitation estimation is of great importance for operational large-scale flood forecasting and drought monitoring. The state-of-the-art precipitation post-processing model is based on a deterministic approach to construct relationships between satellites estimates and ground observations. We propose a probabilistic postprocessor, the Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates using Quantile Regression Forests (QRF4P-NRT), based on quantile modeling, yielding both deterministic and probabilistic predictions. The experimental design incorporates different solutions of near-real-time predictors to further improve the model performance. Using the Integrated Multi-satellitE Retrievals Early Run for Global Precipitation Measurement Mission (IMERG-E) product as an example, we illustrate that the proposed method significantly improves the overall quality of the raw IMERG-E and is also superior to the bias-corrected product (IMERG Final Run, IMERG-F) at daily scale in a complex mountain basin. Evaluations of the corrected IMERG-E, raw IMERG-E, and IMERG-F using ground observation show that the corrected IMERG-E improves correlation coefficients (0.7), mean error (-0.14 mm/day) and root mean square error (3.3 mm/day) relative to the raw IMERG-E (0.31, -0.72 and 5.5 mm/day) and IMERG-F (0.34, -0.09 and 6.0 mm/day). The error decomposition further confirms that the QRF4P-NRT improves on the various deficiencies of the raw IMERG-E product. The ensemble assessment also demonstrates that the quantile outputs provide reliable prediction spread and sharp prediction intervals. The promising results indicate the great potential of the proposed method for probabilistic post-processing for near-real-time satellite precipitation estimates, and for further applications such as hydrological ensemble forecasting.

54 ENVIRONMENTAL SCIENCES↗

Deterministic and Monte Carlo Nuclear Data Adjustment Methods [Slides]

For the Bayesian Monte Carlo methodology, a need to understand convergence of the posterior moments as a function of the number of parameter realizations is required. In high-dimensional systems, it can be very costly to sample entire parameter space and perform functional evaluation for every realization. Bayesian Monte Carlo allows one to relax the GLLS approximations of model linearity and prior/posterior PDF shape. The Bayesian Stochastic Collocation Method is a deterministic approach to “sample” the parameter space. It allows one to relax the GLLS approximations of model linearity and posterior PDF shape. Higher-order posterior moments (i.e., skewness, kurtosis, etc.) can be studied through polynomial expansion. Tensor product quadrature scales poorly and can use sparse grid quadrature methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Gamow-shell-model description of Li isotopes and their mirror partners

Background: Weakly bound and unbound nuclei close to particle drip lines are laboratories of new nuclear structure physics at the extremes of neutron/proton excess. The comprehensive description of these systems requires an open quantum system framework that is capable of treating resonant and nonresonant many-body states on equal footing. Purpose: In this work, we develop the complex-energy configuration interaction approach to describe binding energies and spectra of selected 5 ≤ $\textit{A}$ ≤ 11 nuclei. Method: We employ the complex-energy Gamow shell model (GSM) assuming a rigid 4 He core. The effective Hamiltonian, consisting of a core-nucleon Woods-Saxon potential and a simplified version of the Furutani-Horiuchi-Tamagaki interaction with the mass-dependent scaling, is optimized in the $\textit{sp}$ space. To diagonalize the Hamiltonian matrix, we employ the Davidson method and the Density Matrix Renormalization Group technique. Results: We report our optimized GSM Hamiltonian offers a good reproduction of binding energies and spectra with the root-mean-square (rms) deviation from experiment of 160 keV. Since the model performs well when used to predict known excitations that have not been included in the fit, it can serve as a reliable tool to describe poorly known states. A case in point is our prediction for the pair of unbound mirror nuclei 10 Li – 10 N in which a huge Thomas-Ehrman shift dramatically alters the pattern of low-energy excitations. Conclusion: The new model will enable comprehensive studies of structure and reactions aspects of light drip-line nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Accurate Prediction of Algal Biomass Lipid, Protein, and Carbohydrate Composition with Machine Learning Regression Modelling of Near-IR Spectra

During large scale algal biomass cultivation, it is difficult to reliably control relative composition to target levels. Rapid determination of chemical composition is feasible by using near infrared (NIR) spectral data. We sought to build and improve on reliable high-throughput screening prediction method based on partial least squares regression (PLSR) by the application of artificial neural networks (ANN) and associated optimization strategies. The algal biomass sample set was designed and created in an iterative process of culturing in physiologically diverse conditions at the GAI field site, followed by compositional analyses at NREL. The workflow allowed us to identify gaps in compositional space for informing the subsequent cultivation and sampling efforts and generated a high quality set of 210 unique samples with chemical analysis results, spectral scanning data, and cultivation metadata. We observed a significant improvement in the performance of carbohydrate content predictions using an optimized ANN model compared to PLSR, with > 16% reduction in mean absolute percent error (MAPE) when tested on the same set of reserved data. The optimized ANN models for FAME and protein prediction performed exceptionally well with 5.99% and 5.09% MAPE, respectively. Application of these methods to detection and quantification of minor biomass constituents that are relevant to certain product streams has shown positive preliminary results, opening the possibility for extensions to the outputs of this powerful data type. All models are accompanied by prediction uncertainties and unsupervised spectral outlier detection to alert an operator to unreliable spectral data. These tools can be deployed for rapid determination of algal culture status, and cultivation and biomass quality improvement.

algal biofuels↗

Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach

In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In general, the Koopman operator is obtained as a solution to a least-squares problem, and as such, the Koopman operator can be expressed as a closed-form solution that involves the computation of Moore-Penrose inverse of a matrix. For high dimensional systems and also if the size of the obtained data-set is large, the computation of the Moore-Penrose inverse becomes computationally challenging. In this paper, we provide an algorithm for computing the Koopman operator for high dimensional systems in a time-efficient manner. We further demonstrate the efficacy of the proposed approach on two different systems, namely a network of coupled oscillators (with state-space dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204 and up to 24,000 time-points).

Sinha, Subhrajit↗

Efficient Space–Time Reduced Order Model for Linear Dynamical Systems in Python Using Less than 120 Lines of Code

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than 10−5 for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve O(10−3) to O(10−4) relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve O(10) online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.

97 MATHEMATICS AND COMPUTING↗

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗

Spatio–Temporal Coarse–Graining Decomposition of the Global Ocean Geostrophic Kinetic Energy

We expand on a recent determination of the first global energy spectrum of the ocean’s surface geostrophic circulation using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales (> 1000 km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100–500 km) have a root-mean-square (rms) velocity of ~15 cm/s, which increases to ~30–40 cm/s locally in the Gulf Stream and Kuroshio and to ~16–28 cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that ≈25–50% of total geostrophic energy is at scales smaller than 100 km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean circulation show that most of its energy (up to 70%) resides in stationary eddies with characteristic scales smaller than (< 500 km). This highlights the preponderance of ‘standing’ small-scale structures in the global ocean due to the temporally coherent forcing by boundaries. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at ≈200 km and ≈2–3 weeks.

54 ENVIRONMENTAL SCIENCES↗

Representation of Leaf-to-Canopy Radiative Transfer Processes Improves Simulation of Far-Red Solar-Induced Chlorophyll Fluorescence in the Community Land Model Version 5

Recent advances in satellite observations of solar-induced chlorophyll fluorescence (SIF) provide a new opportunity to evaluate and constrain the simulation of terrestrial gross primary productivity (GPP). Accurate representation of the processes driving SIF emission and the radiative transfer of SIF to remote sensing sensors is an essential prerequisite for the evaluation and data assimilation. Recently, SIF simulations have been incorporated into several land surface models, but the scaling of SIF from leaf-level to canopy level is usually not well-represented. In this work, we incorporate the simulation of far-red SIF observed at nadir into the Community Land Model version 5 (CLM5). An efficient and accurate method based on escape probability is developed to scale SIF from leaf-level to top-of-canopy while taking clumping and the radiative transfer processes into account. SIF simulated by CLM5 and a canopy-level model agreed well at sites except one in needle leaf forest (R2>0.91, root-mean-square error < 0.19W m -2 sr -1 um -1 ), and captured the day-to-day variation of tower-measured SIF at temperate forest sites (R 2 >0.68). At the global scale, simulated SIF generally captured the spatial and seasonal pat37 terns of satellite-observed SIF (R2 > 0.76 except for tropical forest). Factors including the fluorescence emission model, clumping, bidirectional effect, and canopy properties (leaf optical properties and leaf area index) had considerable impacts on SIF simulation, and the discrepancies between simulated and observed SIF varied with plant functional type. By improving the representation of radiative transfer for SIF simulation, our model allows better comparisons between simulated and observed SIF towards constraining and evaluating GPP simulations.

59 BASIC BIOLOGICAL SCIENCES↗

Exploring Li-Ion Transport Properties of Li 3 TiCl 6 : A Machine Learning Molecular Dynamics Study

We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li 3 TiCl 6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, deep neural network method and data generated by ab − initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. From MSD analysis, we captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. Similarly, the self and distinct parts of Li-ion dynamics were used to determine Haven’s ratio to describe the Li-ion transport mechanism in Li 3 TiCl 6 . Obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the combination of machine-learning methods and AIMD simulations explains the intricate electrochemical properties of the Li 3 TiCl 6 cathode with remarkably reduced computational time. Thus, our work strongly suggests that the deep neural network-based MLFF could be a promising method for large-scale complex materials.

Selvaraj, Selva Chandrasekaran (ORCID:000000029023↗

Advancements in reflected target nonintrusive assessment (ReTNA) for large optical surface measurement

Reflected computer vision targets are a powerful tool for measurement of mirror surface shape, with several important advantages over traditional fringe deflectometry methods. This method was first presented in 2021 and has undergone significant improvement and demonstration since. We describe a new baseline system using reflected computer vision targets, and present results from a large-scale measurement campaign conducted on both commercial heliostats and test mirrors in the laboratory. Calibration of the measurement system with photogrammetry allows for accurate measurement without careful control of target shape or camera position. Overall, the results show that a baseline setup using this method achieves measurement uncertainties in the slope error root-mean-square less than ±0.11 milliradian due to a series of repeatability conditions, varying sample position, rotation, lighting, camera settings, and system rebuild and recalibration. We present a detailed description of the setup, the results generated by this measurement tool, repeated measurement results, and the strengths and limitations of this metrology system.

14 SOLAR ENERGY↗

Simulations and Experimental Verifications of an Algorithm for Radiation Source Mapping and Navigational Path Generation

Accurate and efficient mapping and localization of both ionizing and non-ionizing radiation sources are important across many different fields. As such, a versatile mapping and navigational path generation algorithm, which can be applied to any point source measurements that follow an inverse-square characteristic, was developed using non-linear least squares methods. Forty thousand simulations were performed on the algorithm, which located sources successfully in a 10 m × 10 m × 10 m three-dimensional space with a success rate of over 80% across different noise functions, given a proportional constant of 10 to 1,000. The algorithm was also verified experimentally with small-scale radioactive decontamination of a 70 cm × 70 cm surface and localization of a lost Wi-Fi router in a 70 m × 70 m open field. One hundred twenty-one measurements were taken from each experiment, which were then fed into the algorithm for navigation. For the radioactive 137Cs source, the estimated locations were within 7 cm × 7 cm of the answer in 79.3% of the scenarios, while the Wi-Fi router was located to within 7 m × 7 m in 57.9% of the tests. In general, the method requires much less information and data than a geographically comprehensive survey and thus shows a lot of potential for practical applications, such as lost source retrieval with unmanned aerial vehicles, small-scale decontamination, mapping undocumented Wi-Fi routers or radio towers, and radiation simulation with radio signals. Here, the different failure modes, desirable features, and potential improvements were also identified but remain as future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗