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DOE OSTI2021

Removing the Effects of Tropical Dynamics from North Pacific Climate Variability

Teleconnections from the Tropics energize variations of the North Pacific climate, but detailed diagnosis of this relationship has proven difficult. Simple univariate methods, such as regression on El Niño-Southern Oscillation (ENSO) indices, may be inadequate since the key dynamical processes involved -- including ENSO diversity in the Tropics, re-emergence of mixed layer thermal anomalies, and oceanic Rossby wave propagation in the North Pacific -- have a variety of overlapping spatial and temporal scales. Here we use a multivariate Linear Inverse Model to quantify tropical and extra-tropical multi-scale dynamical contributions to North Pacific variability, in both observations and CMIP6 models. In observations, we find that the Tropics are responsible for almost half of the seasonal variance, and almost three quarters of the decadal variance, along the North American coast and within the subtropical front region northwest of Hawaii. SST anomalies that are generated by local dynamics within the Northeast Pacific have much shorter time scales, consistent with transient weather forcing by Aleutian low anomalies. Variability within the Kuroshio-Oyashio Extension (KOE) region is considerably less impacted by the Tropics, on all time scales. Consequently, without tropical forcing the dominant pattern of North Pacific variability would be a KOE pattern, rather than the Pacific Decadal Oscillation (PDO). In contrast to observations, most CMIP6 historical simulations produce North Pacific variability that maximizes in the KOE region, with amplitude significantly higher than observed. Correspondingly, the simulated North Pacific in all CMIP6 models is shown to be relatively insensitive to the Tropics, with a dominant spatial pattern generally resembling the KOE pattern, not the PDO.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Patch2Self2: Self-supervised Denoising on Coresets via Matrix Sketching

Diffusion MRI (dMRI) non-invasively maps brain white matter yet necessitates denoising due to low signal-to-noise ratios. Patch2Self (P2S) employing self-supervised techniques and regression on a Casorati matrix effectively denoises dMRI images and has become the new de-facto standard in this field. P2S however is resource intensive both in terms of running time and memory usage as it uses all voxels (n) from all-but-one held-in volumes (d-1) to learn a linear mapping Phi : \mathbb R ^ n x(d-1) \mapsto \mathbb R ^ n for denoising the held-out volume. The increasing size and dimensionality of higher resolution dMRI acquisitions can make P2S infeasible for large-scale analyses. This work exploits the redundancy imposed by P2S to alleviate its performance issues and inspect regions that influence the noise disproportionately. Specifically this study makes a three-fold contribution: (1) We present Patch2Self2 (P2S2) a method that uses matrix sketching to perform self-supervised denoising. By solving a sub-problem on a smaller sub-space so called coreset we show how P2S2 can yield a significant speedup in training time while using less memory. (2) We present a theoretical analysis of P2S2 focusing on determining the optimal sketch size through rank estimation a key step in achieving a balance between denoising accuracy and computational efficiency. (3) We show how the so-called statistical leverage scores can be used to interpret the denoising of dMRI data a process that was traditionally treated as a black-box. Experimental results on both simulated and real data affirm that P2S2 maintains denoising quality while significantly enhancing speed and memory efficiency achieved by training on a reduced data subset.

Fadnavis, Shreyas↗

DOE OSTI2023

Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data

Significant advancement in Bayesian inference of nuclear equation of state (EOS) from gravitational wave and x-ray observations of neutron stars (NSs) has been made by the nuclear astrophysics community especially since GW170817. By extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not), we search for a data-driven and robust empirical formula for the radius 𝑅 1.4 of canonical NSs in terms of the characteristic EOS parameters (features). We also identify the single most important but currently poorly known EOS parameter for determining the 𝑅 1.4 . Using three regression-model-building methodologies: bidirectional stepwise feature selection, least absolute shrinkage selection operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding 𝑅 1.4 values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable 𝑅 1.4 formulas with varying statistical accuracy and technical complexity. Here, the most important EOS parameters for determining 𝑅 1.4 are found consistently in each of the feature selection processes to be (in order of decreasing importance): curvature 𝐾 sym , slope 𝐿, skewness 𝐽 sym of nuclear symmetry energy, skewness 𝐽 0 , incompressibility 𝐾 0 of symmetric nuclear matter, and the magnitude 𝐸 sym ⁡(𝜌 0 ) of symmetry energy at the saturation density 𝜌 0 of nuclear matter.

Bayesian methods↗

DOE OSTI2022

Power counting energy flow polynomials

Power counting is a systematic strategy for organizing collider observables and their associated theoretical calculations. In this paper, we use power counting to characterize a class of jet substructure observables called energy flow polynomials (EFPs). EFPs provide an overcomplete linear basis for infrared-and-collinear safe jet observables, but it is known that in practice, a small subset of EFPs is often sufficient for specific jet analysis tasks. By applying power counting arguments, we obtain linear relationships between EFPs that hold for quark and gluon jets to a specific order in the power counting. We test these relations in the parton shower generator Pythia, finding excellent agreement. Power counting allows us to truncate the basis of EFPs without affecting performance, which we corroborate through a study of quark-gluon tagging and regression.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Image-Driven Hybrid Structural Analysis Based on Continuum Point Cloud Method with Boundary Capturing Technique

Conventional approaches for the structural health monitoring of infrastructures often rely on physical sensors or targets attached to structural members, which require considerable preparation, maintenance, and operational effort, including continuous on-site adjustments. This paper presents an image-driven hybrid structural analysis technique that combines digital image processing (DIP) and regression analysis with a continuum point cloud method (CPCM) built on a particle-based strong formulation. Polynomial regressions capture the boundary shape change due to the structural loading and precisely identify the edge and corner coordinates of the deformed structure. The captured edge profiles are transformed into essential boundary conditions. This allows the construction of a strongly formulated boundary value problem (BVP), classified as the Dirichlet problem. Capturing boundary conditions from the digital image is novel, although a similar approach was applied to the point cloud data. It was shown that the CPCM is more efficient in this hybrid simulation framework than the weak-form-based numerical schemes. Unlike the finite element method (FEM), it can avoid aligning boundary nodes with regression points. A three-point bending test of a rubber beam was simulated to validate the developed technique. The simulation results were benchmarked against numerical results by ANSYS and various relevant numerical schemes. The technique can effectively solve the Dirichlet-type BVP, yielding accurate deformation, stress, and strain values across the entire problem domain when employing a linear strain model and increasing the number of CPCM nodes. In addition, comparative analysis with conventional displacement tracking techniques verifies the developed technique’s robustness. The proposed technique effectively circumvents the inherent limitations of traditional monitoring methods resulting from the reliance on physical gauges or target markers so that a robust and non-contact solution for remote structural health monitoring in real-scale infrastructures can be provided, even in unfavorable experimental environments.

Chemistry↗

DOE OSTI2021

Radiation effects on atherosclerosis in atomic bomb survivors: a cross-sectional study using structural equation modeling

Past reports indicated that total-body irradiation at low to moderate doses could be responsible for cardiovascular disease risks, but the mechanism remains unclear. The purpose of this study was to investigate the association between radiation exposure and atherosclerosis, an underlying pathology of cardiovascular diseases, in the Japanese atomic bomb survivors. We performed a cross-sectional study measuring 14 clinical-physiological atherosclerosis indicators during clinical exams from 2010 to 2014 in 3274 participants of the Adult Health Study cohort. Multivariable analyses were performed by using a structural equation model with latent factors representing underlying atherosclerotic pathologies: (1) arterial stiffness, (2) calcification, and (3) plaque as measured with indicators chosen a priori on the basis of clinical-physiological knowledge. Radiation was linearly associated with calcification (standardized coefficient per Gy 0.15, 95 % confidence interval: CI [0.070, 0.23]) and plaque (0.11, 95 % CI [0.029, 0.20]), small associations that were comparable to about 2 years of aging per Gy of radiation exposure, but not with arterial stiffness (0.036, 95 % CI [-0.025, 0.095]). The model fitted better and had narrower confidence intervals than separate ordinary regression models explaining individual indicators independently. The associations were less evident when the dose range was restricted to a maximum of 2 or 1 Gy. By combining individual clinical-physiological indicators that are correlated because of common, underlying atherosclerotic pathologies, we found a small, but significant association of radiation with atherosclerosis.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A behavior and physiology-based decision support tool to predict thermal comfort and stress in non-pregnant, mid-gestation, and late-gestation sows

Background: Although thermal indices have been proposed for swine, none to our knowledge differentiate by reproductive stage or predict thermal comfort using behavioral and physiological data. The study objective was to develop a behavior and physiology-based decision support tool to predict thermal comfort and stress in multiparous (3.28 ± 0.81) non-pregnant (n = 11), mid-gestation (n = 13), and late-gestation (n = 12) sows. Results: Regression analyses were performed using PROC MIXED in SAS 9.4 to determine the optimal environmental indicator [dry bulb temperature (T DB ) and dew point] of heat stress (HS) in non-pregnant, mid-gestation, and late-gestation sows with respiration rate (RR) and body temperature (T B ) successively used as the dependent variable in a cubic function. A linear relationship was observed for skin temperature (T S ) indicating that TDB rather than the sow HS response impacted TS and so TS was excluded from further analyses. Reproductive stage was significant for all analyses (P < 0.05). Heat stress thresholds for each reproductive stage were calculated using the inflections points of RR for mild HS and T B for moderate and severe HS. Mild HS inflection points differed for non-pregnant, mid-gestation, and late gestation sows and occurred at 25.5, 25.1, and 24.0 °C, respectively. Moderate HS inflection points differed for non-pregnant, mid-gestation, and late gestation sows and occurred at 28.1, 27.8, and 25.5 °C, respectively. Severe HS inflection points were similar for non-pregnant and mid-gestation sows (32.9 °C) but differed for late-gestation sows (30.8 °C). These data were integrated with previously collected behavioral thermal preference data to estimate the T DB that non-pregnant, mid-gestation, and late-gestation sows found to be cool (T DB < T DB preference range), comfortable (T DB = T DB preference range), and warm (T DB preference range < T DB < mild HS). Conclusions: The results of this study provide valuable information about thermal comfort and thermal stress thresholds in sows at three reproductive stages. The development of a behavior and physiology-based decision support tool to predict thermal comfort and stress in non-pregnant, mid-gestation, and late-gestation sows is expected to provide swine producers with a more accurate means of managing sow environments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Reinforcement Learning via Gaussian Processes with Neural Network Dual Kernels

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Stoichiometrically-informed symbolic regression for extracting chemical reaction mechanisms from data

A data-driven computational method is introduced to extract chemical reaction mechanisms from time series chemical concentration data. It is realized through the use of dynamic symbolic regression in which a sparse analytical form for a dynamical system is discoverable from the underlying data. We specifically develop the stoichiometrically-informed symbolic regression (SISR) method to address a standing challenge in complex chemical reaction networks: given a time-series dataset of concentrations of several components, what is the mechanism and the associated rate constants? SISR finds the optimal mechanism, kinetic equations and rate constants by combining differential optimization with a genetic optimization approach that searches a symbolic space of possible reaction mechanisms. Use of SISR in several paradigmatic examples spanning linear and nonlinear reaction schemes results in excellent agreement between true and predicted mechanisms, including when the method is applied to noisy data. The advantages of a stoichiometrically-informed approach such as SISR to address reaction discovery is illustrated through comparison with the use of generic state-of-the-art data-driven approaches.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Differential credibility assessment for statistical downscaling

Climate science is increasingly using (i) ensembles of climate projections from multiple models derived using different assumptions and/or scenarios and (ii) process-oriented diagnostics of model fidelity. Efforts to assign differential credibility to projections and/or models are also rapidly advancing. A framework to quantify and depict the credibility of statistically downscaled model output is presented and demonstrated. Here, the approach employs transfer functions in the form of robust and resilient generalized linear models applied to downscale daily minimum and maximum temperature anomalies at 10 locations using predictors drawn from ERA-Interim reanalysis and two global climate models (GCM; GFDL-ESM2M and MPI-ESM-LR). The downscaled time series are used to derive several impact relevant CLIMDEX temperature indices that are assigned credibility based on (1) the reproduction of relevant large-scale predictors by the GCMs (i.e. fraction of regression beta-weights derived from predictors that are well-reproduced) and (2) the degree of variance in the observations reproduced in the downscaled series following application of a new variance inflation technique. Credibility of the downscaled predictands varies across locations, between the two GCM and is generally higher for minimum temperature than maximum temperature. The differential credibility assessment framework demonstrated here is easy to use and flexible. It can be applied as is to inform decision makers regarding projection confidence, and/or extended to include other components of the transfer functions, and/or used to weight members of a statistically downscaled ensemble.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Younger facial looks are associate with a lower likelihood of several age-related morbidities in the middle-aged to elderly

Abstract Background Looking older for one’s chronological age is associated with a higher mortality rate. Yet it remains unclear how perceived facial age relates to morbidity and the degree to which facial ageing reflects systemic ageing of the human body. Objectives To investigate the association between ΔPA and age-related morbidities of different organ systems, where ΔPA represents the difference between perceived age (PA) and chronological age. Methods We performed a cross-sectional analysis on data from the Rotterdam Study, a population-based cohort study in the Netherlands. High-resolution facial photographs of 2679 men and women aged 51.5–87.8 years of European descent were used to assess PA. PA was estimated and scored in 5-year categories using these photographs by a panel of men and women who were blinded for chronological age and medical history. A linear mixed model was used to generate the mean PAs. The difference between the mean PA and chronological age was calculated (ΔPA), where a higher (positive) ΔPA means that the person looks younger for their age and a lower (negative) ΔPA that the person looks older. ΔPA was tested as a continuous variable for association with ageing-related morbidities including cardiovascular, pulmonary, ophthalmological, neurocognitive, renal, skeletal and auditory morbidities in separate regression analyses, adjusted for age and sex (model 1) and additionally for body mass index, smoking and sun exposure (model 2). Results We observed 5-year higher ΔPA (i.e. looking younger by 5 years for one’s age) to be associated with less osteoporosis [odds ratio (OR) 0.76, 95% confidence interval (CI) 0.62–0.93], less chronic obstructive pulmonary disease (OR 0.85, 95% CI 0.77–0.95), less age-related hearing loss (model 2; B = −0.76, 95% CI −1.35 to −0.17) and fewer cataracts (OR 0.84, 95% CI 0.73–0.97), but with better global cognitive functioning (g-factor; model 2; B = 0.07, 95% CI 0.04–0.10). Conclusions PA is associated with multiple morbidities and better cognitive function, suggesting that systemic ageing and cognitive ageing are, to an extent, externally visible in the human face.

Mekić, Selma↗

DOE OSTI2022

Star–Galaxy Image Separation with Computationally Efficient Gaussian Process Classification

Abstract We introduce a novel method for discerning optical telescope images of stars from those of galaxies using Gaussian processes (GPs). Although applications of GPs often struggle in high-dimensional data modalities such as optical image classification, we show that a low-dimensional embedding of images into a metric space defined by the principal components of the data suffices to produce high-quality predictions from real large-scale survey data. We develop a novel method of GP classification hyperparameter training that scales approximately linearly in the number of image observations, which allows for application of GP models to large-size Hyper Suprime-Cam Subaru Strategic Program data. In our experiments, we evaluate the performance of a principal component analysis embedded GP predictive model against other machine-learning algorithms, including a convolutional neural network and an image photometric morphology discriminator. Our analysis shows that our methods compare favorably with current methods in optical image classification while producing posterior distributions from the GP regression that can be used to quantify object classification uncertainty. We further describe how classification uncertainty can be used to efficiently parse large-scale survey imaging data to produce high-confidence object catalogs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗

DOE OSTI2020

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Harnessing Machine Learning to Predict MoS 2 Solid Lubricant Performance

Physical vapor deposited (PVD) molybdenum disulfide (MoS 2 ) solid lubricant coatings are an exemplar material system for machine learning methods due to small changes in process variables often causing large variations in microstructure and mechanical/tribological properties. Here, in this work, a gradient boosted regression tree machine learning method is applied to an existing experimental data set containing process, microstructure, and property information to create deeper insights into the process-structure–property relationships for molybdenum disulfide (MoS 2 ) solid lubricant coatings. The optimized and cross-validated models show good predictive capabilities for density, reduced modulus, hardness, wear rate, and initial coefficients of friction. The contribution of individual deposition variables (i.e., argon pressure, deposition power, target conditioning) on coating properties is highlighted through feature importance. The process-property relationships established herein show linear and non-linear relationships and highlight the influence of uncontrolled deposition variables (i.e., target conditioning) on the tribological performance.

MoS2↗

DOE OSTI2024

Model and remote-sensing-guided experimental design and hypothesis generation for monitoring snow-soil–plant interactions

In this study, we develop a machine-learning (ML)-enabled strategy for selecting hillslope-scale ecohydrological monitoring sites within snow-dominated mountainous watersheds, with a particular focus on snow-soil–plant interactions. Data layers rely on spatial data layers from both remote sensing and hydrological model simulations. Specifically, a Landsat-based foresummer drought sensitivity index is used to define the dependency of the annual peak plant productivity on the Palmer drought severity index in the early growing season. Hydrological simulations provide the spatiotemporal dynamics of near-surface soil moisture and snow depth. In this framework, a regression analysis identifies the key hydrological variables relevant to the spatial heterogeneity of drought sensitivity. We then apply unsupervised clustering to these key variables, using the Gaussian mixture model, to group hillslopes into several zones that have divergent relationships regarding soil moisture, snow dynamics, and drought sensitivity. Using the datasets collected in the East River Watershed (Crested Butte, Colorado, United States), results show that drought sensitivity is significantly correlated with model-derived soil moisture and snow-free timing over space and time. The relationship is, however, non-linear, such that the correlation decreases above a threshold elevation and in a heavy snow year due to large snowpacks, lateral flow, and soil storage limitations. Clustering is then able to define the zones that have high or low sensitivity to drought, as well as the mid-elevation regions where sensitivity is associated with the topographic aspect and net potential radiation. In addition, the algorithm identifies the most representative hillslopes with road/trail access within each zone for installing monitoring sites. Our method also aims to significantly increase the use of ML and model-simulation results to guide critical zone and watershed monitoring activities.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Insights into cosmological structure formation with machine learning.

Our modern understanding of cosmological structure formation posits that small matter density fluctuations present in the early Universe, as traced by the cosmic microwave background, grow via gravitational instability to form extended haloes of dark matter. A theoretical understanding of the structure, evolution and formation of dark matter haloes is an essential step towards unravelling the intricate connection between halo and galaxy formation, needed to test our cosmological model against data from upcoming galaxy surveys. Physical understanding of the process of dark matter halo formation is made difficult by the highly non-linear nature of the haloes' evolution. I describe a new approach to gain physical insight into cosmological structure formation based on machine learning. This approach combines the ability of machine learning algorithms to learn non-linear relationships, with techniques that enable us to physically interpret the learnt mapping. I describe applicatio ns of th e method, with the aim of investigating which aspects of the early universe density field impact the later formation of dark matter haloes. First I present a case where the process of halo formation is turned into a binary classification problem; the algorithm predicts whether or not dark matter `particles' in the initial conditions of a simulation will collapse into haloes of a given mass range. Second, I present its generalization to regression, where the algorithm infers the final mass of the halo to which each particle will later belong. I show that the initial tidal shear does not play a significant role compared to the initial density field in establishing final halo masses. Finally, I demonstrate that extending the framework to deep learning algorithms such as convolutional neural networks allows us to explore connections between the early universe and late time haloes beyond those studied by existing analytic approximations of halo collapse.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗