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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Variational quantum algorithm for estimating the quantum Fisher information

The quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this paper we present a variational quantum algorithm called variational quantum Fisher information estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds with literature bounds and show that our bounds are tighter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis

Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

Markov chain Monte Carlo↗
DOE OSTI2023

Soil fertility and drought interact to determine large variations in wood production for a hyperdominant Amazonian tree species

The productivity of the Amazon Rainforest is related to climate and soil fertility. However, the degrees to which these interactions influence multiannual to decadal variations in tree diameter growth are still poorly explored. To fill this gap, we used radiocarbon measurements to evaluate the variation in tree growth rates over the past decades in an important hyperdominant species, Eschweilera coriacea (Lecythidaceae), from six sites in the Brazilian Amazon that span a range of soil properties and climate. Using linear mixed-effects models, we show that temporal variations in mean annual diameter increment evaluated over a specific time period reflect interactions between soil fertility and the drought index (SPEI-Standardized Precipitation and Evapotranspiration Index). Our results indicate that the growth response of trees to drought is strongly dependent on soil conditions, a facet of forest productivity that is still underexplored, and which has great potential for improving predictions of future tropical tree growth in the face of projected climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Genomic variation within the maize stiff-stalk heterotic germplasm pool

The stiff-stalk heterotic group in Maize (Zea mays L.) is an important source of inbreds used in U.S. commercial hybrid production. Founder inbreds B14, B37, B73, and, to a lesser extent, B84, are found in the pedigrees of a majority of commercial seed parent inbred lines. We created high-quality genome assemblies of B84 and four expired Plant Variety Protection (ex-PVP) lines LH145 representing B14, NKH8431 of mixed descent, PHB47 representing B37, and PHJ40, which is a Pioneer Hi-Bred International (PHI) early stiff-stalk type. Sequence was generated using long-read sequencing achieving highly contiguous assemblies of 2.13-2.18 Gbp with N50 scaffold lengths >200 Mbp. Inbred-specific gene annotations were generated using a core five-tissue gene expression atlas, whereas transposable element (TE) annotation was conducted using de novo and homology-directed methodologies. Compared with the reference inbred B73, synteny analyses revealed extensive collinearity across the five stiff-stalk genomes, although unique components of the maize pangenome were detected. Comparison of this set of stiff-stalk inbreds with the original Iowa Stiff Stalk Synthetic breeding population revealed that these inbreds represent only a proportion of variation in the original stiff-stalk pool and there are highly conserved haplotypes in released public and ex-Plant Variety Protection inbreds. Despite the reduction in variation from the original stiff-stalk population, substantial genetic and genomic variation was identified supporting the potential for continued breeding success in this pool. The assemblies described here represent stiff-stalk inbreds that have historical and commercial relevance and provide further insight into the emerging maize pangenome.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Little vertical and circumferential variations in stem xylem water Δ 2 H and Δ 18 O in three tree species

Vertical and circumferential patterns of xylem water isotope signatures in large trees are rarely characterized but may influence interpretation of water source investigations and soil/xylem water isotope offsets. Furthermore, to examine vertical and circumferential variation in xylem water δ 2 H and δ 18 O, we collected xylem tissue at 5 heights (0, 1, 4, 7 and 10 m) from three replicate trees of three species with contrasting xylem anatomy, two angiosperms (Liquidambar styraciflua and Quercus nigra) and one gymnosperm (Pinus taeda). Concurrently, we also determined δ 2 H and δ 18 O of groundwater, soil water, and recent precipitation. On a different day, we collected circumferential samples at 1 m from the same trees to test for sectorality effects. Water from stem and soil samples were cryogenically extracted and analyzed for δ 2 H and δ 18 O. Mean xylem water δ 2 H and δ 18 O were significantly different between species, both vertically and circumferentially. We did not find significant (p = 0.05) systematic variation in δ 2 H or δ 18 O with height. We found no significant evidence for sectorality effects on δ 2 H, δ 18 O. Variances of vertical synoptic xylem water δ 2 H or δ 18 O were similar between species, 7.2–10.4‰ for δ 2 H and 0.58–0.81‰ for δ 18 O. Circumferential variances were also similar between species, 4.0–6.0 for δ 2 H and 0.37–0.44 for δ 18 O. A mixing model showed that sweetgum, water oak and loblolly pine, were drawing most of their water from deep soil from 45 to 190 cm (84.7, 68.4 and 53.2%, respectively) however, soil water-excess values indicate δ 2 H fractionation effects on these estimates. Dual isotope mixing model evaluation with single and multiple sample configurations showed that source water estimates were not affected by within tree variability of xylem water signatures. Xylem water δ 2 H and δ 18 O variability with height or circumference, was 3.2 and 2.7 times less than between tree variation because of transient temporal and spatial processes and is, therefore, not likely to affect interpretations of water sourcing in these three species.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

What explains the year-to-year variation in growing season timing of boreal black spruce forests?

Amplified climate warming in high latitudes is expected to affect growing season timing of the vast boreal biome. It is unclear whether the presence of permafrost (perennially frozen ground) might have an influence on changes in growing season timing. Here, this study examined how different environmental variables explained, either directly or indirectly, the variation in growing season timing of boreal forest stands with and without permafrost. We expected that environmental variables explaining the variation in growing season timing differed or had different explanatory power depending on permafrost presence or absence. The growing season was delineated from daily gross primary productivity (GPP) time series derived from 40 site-year data of net ecosystem carbon dioxide exchange measured with eddy covariance techniques over five black spruce (Picea mariana [Mill.])-dominated boreal forest stands in North America. In permafrost-free forest stands, a combination of start in canopy ‘green-up’ in spring and the timing of air and soil temperature increasing above freezing explained the start-of-season (SOS GPP ). Results from commonality analysis and structural equation modeling suggest that canopy ‘green-up’ and air temperature directly affected SOS GPP in permafrost-free forest stands. In addition, soil temperature acted as mediator for an indirect effect of air temperature on SOS GPP . In contrast, none of the environmental variables, or their combination, explained the variation in SOS GPP in forest stands with permafrost. The explanatory power of environmental variables was more consistent regarding the end-of-season (EOS GPP ). In both, forest stands with and without permafrost, EOS GPP was directly explained by mean soil water content in the fall and the first day of continuous snowpack formation. A better understanding how environmental variables control SOS GPP and EOS GPP in forest stands with and without permafrost will help to refine parameterizations of the boreal biome in Earth system models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

SIF-based GPP modeling for evergreen forests considering the seasonal variation in maximum photochemical efficiency

Solar-induced chlorophyll fluorescence (SIF) has shown great potential in estimating gross primary production (GPP). However, their quantitative relationship is not invariant, which undermines the reliability of empirical SIF-based GPP estimation at fine spatiotemporal scales, especially under extreme conditions. In this study, we developed a parsimonious mechanistic model for SIF-based GPP estimation in evergreen needle forests (ENF) by employing the Mechanistic Light Response framework and Eco-Evolutionary theory to describe the light and dark reactions during photosynthesis, respectively. Specifically, we found that considering the seasonal variation in a key parameter of the MLR framework, the maximum photochemical efficiency of photosystem II (Φ PSIImax ), can avoid the GPP overestimation in winter and early spring due to the relatively low environmental sensitivity of SIF. Compared to the estimates from other benchmark models, our GPP estimates were closer to the 1: 1 line and had higher accuracy (average R 2 = 0.86, RMSE=1.99 μmol m -2 s -1 ) across sites. Furthermore, the changes in the relationship between SIF and J (refers to the electron transport rate) contribute a lot to the dynamic SIF–GPP relationship in this study, while the J–GPP relationship is less variant when the temperature drops. Further, the seasonal variation in the SIF–J relationship, especially the reduction in its slope at low temperatures, is found largely explained by the Φ PSIImax . These results indicate the importance of the uncertainty caused by the variation in the SIF–J relationship for SIF-based GPP estimation, and the consideration of changes in Φ PSIImax under extreme conditions (such as severe winter in this study) is crucial for the improvement of GPP estimation via SIF.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Impact of vertical and seasonal variation in leaf traits on simulating soybean canopy photosynthesis via 1D and 3D modeling

Accurate modeling of photosynthesis is crucial for predicting crop productivity and quantifying the carbon cycle in agroecosystems. Leaf traits are essential inputs for modeling canopy photosynthesis. Yet, many existing models still use fixed plant functional type (PTF)-based values to parameterize leaf traits under a big-leaf or two-big-leaf assumption, neglecting their vertical profiles and seasonal changes. This simplification may introduce significant uncertainties in estimating gross primary productivity (GPP). In this study, we simulated soybean GPP and tested the effects of vertical and seasonal variation in three key leaf photosynthetic traits: the maximum carboxylation rate at 25 °C (Vcmax 25 ), leaf chlorophyll content (LCC), and leaf mass per area (LMA) in the 1D-SCOPE and 3D-Helios models. Weekly field measurements were conducted during the growing season of 2024 to support the simulation. We designed ten leaf trait parameterization schemes by incorporating different combinations of vertical profiles and seasonal changes, while assuming homogeneous canopy architecture in both models. Our results revealed that Vcmax 25 vertical and seasonal variation had the strongest influence on simulated GPP in both 1D and 3D models, while LCC and LMA effects were minimal. Particularly, the scheme with an empirically parameterized Vcmax 25 profile achieved comparable performance to the scheme with the measured Vcmax 25 profile. Both 1D-SCOPE and 3D-Helios accurately modeled GPP (SCOPE: R 2 = 0.87, Bias = 0.55 µmol m⁻² s⁻¹; Helios: R 2 = 0.9, Bias = 0.22 µmol m⁻² s⁻¹) under the most complex scheme, and their responses to vertical and seasonal variation in leaf traits were consistent, demonstrating the robustness of our findings. Based on our findings, we propose a scalable framework for parameterizing leaf traits to improve GPP simulations. This study contributes to improving the representation of leaf trait dynamics in canopy-level photosynthesis models, potentially enhancing our ability to predict crop productivity and understand agroecosystem carbon dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Detection of surface water temperature variations of Mongolian lakes benefiting from the spatially and temporally gap-filled MODIS data

Lakes provide critical water resources for human activities and ecosystems, particularly in the Mongolian Plateau (MP), which is characterized by a dry climate and a harsh environment. As a region that is sensitive to anthropogenic warming, tracking lake surface water temperature (LSWT) changes in Mongolian lakes is crucial for understanding the consequences of a warming climate on lake ecosystems. However, the long-term monitoring of LSWT is restricted by the spatiotemporal gaps in the raw imagery of remote sensing-based land surface temperature (LST), e.g., the commonly used Moderate Resolution Imaging Spectroradiometer (MODIS) LST products. This study applied an improved gap-filling method by utilizing the discrete cosine transform-based penalized least squares (DCT-PLS) strategy in the spatial domain combined with the linear interpolation (LI) algorithm in the temporal domain. The method was applied to fill gaps in the LSWT imagery of 12 representative lakes across MP. The randomly sampled high-quality MODIS LSWT values in the spatial and temporal domains were excavated as false data gaps and considered “virtual true” validation datasets. The spatial validation results showed that the estimated LSWT for all the lake cases were comparable with the “virtual true” LSWT values, with the average values of the coefficient of determination, mean absolute error, mean square error, and root mean square error being 0.98, 0.38 °C, 0.45 °C, and 0.59 °C, respectively. Meanwhile, the error of nighttime LSWT results was relatively lower than that of daytime LSWT. For temporal interpolation validation, the LI algorithm exhibited relatively better performance and could more objectively indicate the variation in LSWT. Benefiting from the spatially and temporally well-constrained data, we analyzed the interannual and intra-annual change characteristics of the LSWTs of the 12 lakes. The long-term variations of annual and seasonal mean LSWTs in the 12 selected lakes exhibited no evident trends in 2000–2020, while presented apparent interannual fluctuations. The slight changes in the average LSWTs of the 12 selected lakes were in excellent synchronization with the surrounding LST derived from the reanalysis datasets, confirming the widely reported phenomenon of “global warming hiatus” that occurred in the early 21st century. This study improves the understanding of the LSWT variations in Mongolian lakes in response to global climate change. It has the potential to provide an effective approach for monitoring LSWT changes in other large-scale studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Convection-permitting hindcasting of diurnal variation of Mei-yu rainfall over East China with a global variable-resolution model

Two sets of 48-hr hindcast experiments for Mei-yu season using non-hydrostatic global variable-resolution model (MPAS-Atmosphere) with regional refinement at 4km resolution (V4km) and uniform 60km resolution (U60km) are first-time conducted to attempt at simulating the Mei-yu rainfall in 2015 over East China. The analysis focuses on the seasonal average of diurnal variation of precipitation amount (PA), intensity (PI), and frequency (PF). Both simulations reasonably reproduce the spatial distribution of PA. V4km is more skillful in simulating the spatial distributions and magnitudes of PF and PI. The diurnal cycle of Mei-yu rainfall shows a major early morning peak and a minor afternoon peak, contributed by precipitation during two sub-periods with distinct synoptic circulations. With strong Mei-yu in the first sub-period, the diurnal variation of PA is controlled by nocturnal southwesterly jet. V4km overestimates the morning peak mainly due to its bias in simulating boundary layer inertial oscillation. Although differences in PA between the simulations are small, U60km overestimates PF and underestimates PI. With weak Mei-yu in the second sub-period, the diurnal variation of PA is controlled by both synoptic circulation and local convection. At both resolutions, deviations in the large-scale circulation modulated by a few typhoons lead to positive biases in the morning peak of PA. After removing the typhoon impacts, V4km captures the observed diurnal cycle of PA well, while U60km significantly underestimates PA and PI particularly in the afternoon. Future studies focusing on advancing modeling of southwesterly jet and typhoons may further improve convection permitting simulation of Mei-yu rainfall.

Xu, Mingyue↗
DOE OSTI2022

Spatiotemporal Variations of Evapotranspiration in Amazonia Using the Wavelet Phase Difference Analysis

The relationships and seasonal-to-annual variations among evapotranspiration (ET), precipitation (P), terrestrial water storage anomalies (TWSA), radiation (downward shortwave radiation, DSR), and phenology (leaf area index, LAI) are complex across the Amazon basin. Here, to analyze how ET is controlled by these influencing factors, we used wavelet phase difference (WPD) to investigate the effects of P, TWSA, DSR, and LAI on ET at different spatiotemporal scales. The Amazon-scale averaged ET has strong correlations with these factors at the annual and multi-year periodicities. The patterns of WPDs have south-north and west-east divides due to the significant variation in climatic conditions. The results demonstrate that ET is mainly affected by water and energy availability while vegetation regulates both processes. The deep soil moisture/groundwater can provide strong subsidies to ET during the meteorological dry season in the water-limited area of Amazon. The WPD can well reflect the responses of ET to the variations of P, TWSA, DSR, and LAI, and the process of vegetation sustaining ET in the dry years in the water-limited area of the Amazon.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Potential Vorticity Dynamics Explain How Extratropical Oceans and the Arctic Modulate Wintertime Land–Temperature Variations

Temperature variations across the continental northern hemisphere at the interdecadal scale are thought to be remotely modulated by oceanic internal climate variability and the Arctic. Nevertheless, further elucidating the dynamics is essential for clarifying ongoing debates. We show that potential vorticity (PV) dynamics provide a concise explanation for these teleconnections. Our findings demonstrate that extratropical oceans and the Arctic can remotely modulate the wintertime continental temperature variations by stimulating PV anomalies, which are constrained by climatological PV gradients and jet streams. A causal explanation includes anomalous temperature and precipitation over oceans and the Arctic inducing local PV anomalies via diabatic heating. Subsequently, meridional and downstream advection distributes the anomalous PV to remote land regions where the climatological PV gradients are strong, that is, involving PV fronts, as well as jet streams; therefore, PV fronts and jet streams jointly indicate land regions that are largely and frequently impacted. However, land can also modulate other regions through the same mechanism when variations over land occur in advance. Clear causality depends on which factor is independent, while interactions among those regions may convolute the causality, thereby causing further debates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A universal variational quantum eigensolver for non-Hermitian systems

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$O(log_{2}{N})$$ O ( l o g 2 N ) quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Variational actor-critic algorithms,

We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Variational deep learning of equilibrium transition path ensembles

Here, we present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗