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Constrained Inference with Hidden Markov Models
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Visual Interrogation of Attention-Based Models for Natural Language Inference and Machine Comprehension
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Machine-Learning Accelerated Studies of Materials with High Performance and Edge Computing
In the studies of materials, experimental measurements often serve as the reference to verify physics theory and modeling; while theory and modeling provide a fundamental understanding of the physics and principles behind. However, the interactions and cross validation between them have long been a challenge even to-date. Not only that inferring a physics model from experimental data is itself a difficult inverse problem, another major challenge is the orders-of-magnitude longer wall-clock time required to carry out high-fidelity computer modeling to match the timescale of experiments. We envisage that by combining high performance computing, data science, and edge computing technology, the current predicament can be alleviated, and a new paradigm of data-driven physics research will open up. For example, we can accelerate computer simulations by first performing the large-scale modeling on high performance computers and train a machine-learned surrogate model. This computationally inexpensive surrogate model can then be transferred to the computing units residing closely to the experimental facilities to perform high-fidelity simulations at a much higher throughout. The model will also be more amenable to analyzing and validating experimental observations in comparable time scales at a much lower computational cost. Further integration of these accelerated computer simulations with an outer machine learning loop can also inform and direct future experiments, while making the inverse problem of physics model inference more tractable. We will demonstrate a proof-of-concept by using a quantum Monte Carlo application, Dynamical Cluster Approximation (DCA++), to machine-learn a surrogate model and accelerate the study of quantum correlated materials.
Bayesian operator inference for data-driven reduced-order modeling
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.
DLHub: Simplifying publication, discovery, and use of machine learning models in science
Machine Learning (ML) has become a critical tool enabling new methods of analysis and driving deeper understanding of phenomena across scientific disciplines. There is a growing need for "learning systems" to support various phases in the ML lifecycle. While others have focused on supporting model development, training, and inference, few have focused on the unique challenges inherent in science, such as the need to publish and share models and to serve them on a range of available computing resources. In this paper, we present the Data and Learning Hub for science (DLHub), a learning system designed to support these use cases. Specifically, DLHub enables publication of models, with descriptive metadata, persistent identifiers, and flexible access control. It packages arbitrary models into portable servable containers, and enables low-latency, distributed serving of these models on heterogeneous compute resources. In this work, we show that DLHub supports low-latency model inference comparable to other model serving systems including TensorFlow Serving, SageMaker, and Clipper, and improved performance, by up to 95%, with batching and memoization enabled. We also show that DLHub can scale to concurrently serve models on 500 containers. Finally, we describe five case studies that highlight the use of DLHub for scientific applications.
Late-time mixing and turbulent behavior in high-energy-density shear experiments at high Atwood numbers
The LANL Shear Campaign uses millimeter-scale initially solid shock tubes on the National Ignition Facility to conduct high-energy-density hydrodynamic plasma experiments, capable of reaching energy densities exceeding 100 kJ/cm3. These shock-tube experiments have for the first time reproduced spontaneously emergent coherent structures due to shear-based fluid instabilities [i.e., Kelvin-Helmholtz (KH)], demonstrating hydrodynamic scaling over 8 orders of magnitude in time and velocity. The KH vortices, referred to as “rollers,” and the secondary instabilities, referred to as “ribs,” are used to understand the turbulent kinetic energy contained in the system. Their evolution is used to understand the transition to turbulence and that transition's dependence on initial conditions. Experimental results from these studies are well modeled by the RAGE (Radiation Adaptive Grid Eulerian) hydro-code using the Besnard-Harlow-Rauenzahn turbulent mix model. Information inferred from both the experimental data and the mix model allows us to demonstrate that the specific Turbulent Kinetic Energy (sTKE) in the layer, as calculated from the plan-view structure data, is consistent with the mixing width growth and the RAGE simulations of sTKE.
Earth System Reanalysis in Support of Climate Model Improvements
Recent climate model developments, established through increased model resolution, have led to substantial improvements in model simulations of the time-evolving, coupled Earth system and its subcomponents. However, regardless of resolution, climate models will always produce climate features and variability that differ from the real world and will be prone to biases. This is due to many remaining uncertainties, such as in parametric and structural model uncertainty, in the initial conditions prescribed, and in the prescribed (scenario) forcing which varies on decadal to centennial timescales. Further model improvements are expected to arise specifically from improved representation of physical processes realized through model-data fusion. This will create an unprecedented opportunity to better exploit a large array of Earth observations, from in situ measurements to weather radars and satellite observations, as the resolved scales of the models approach those of the observations. For this, climate DA will be the central tool to bring models and observations into consistency, by improving initial conditions, inferring uncertain model parameters and structure, and quantifying uncertainty. Generally, there will be advantages and complementarities of adjoint-based smoother approaches, ensemble-based filter approaches, or new ML-inspired approaches. Yet, the ever-increasing model resolution will present growing challenges arising from computational cost, calling for new ways of performing data assimilation and model optimization. Using the complementarity in a hybrid approach, blending tools and concepts from variational, ensemble and ML methods might be what is required in the future. In this context ML could be important to handle non-linear responses, and to better approximate non-Gaussian distributions.
Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems
In this work, we compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations, which are then discretized for numerical solution. The second is discrete in time, where one directly infers a discrete-time model in the form of a nonlinear autoregression moving average model. The comparison is performed in a special case where the observations are known to have been obtained from a hypoelliptic stochastic differential equation. We show that the discrete-time approach has better predictive skills, especially when the data are relatively sparse in time. Finally , we discuss open questions as well as the broader significance of the results.
Informing Robust Functional Relationship Benchmarks: An Evaluation of the Temperature Sensitivity of Ecosystem Respiration Across the Arctic-Boreal Region
During land model development, simulated carbon dynamics are often benchmarked against observational data sets to evaluate model performance. Functional relationship benchmarks are the relationship between a driving variable (e.g., temperature) and a response variable (e.g., ecosystem respiration) and are a promising tool for assessing model performance by evaluating modeled sensitivities to changing environmental conditions. However, observed functional relationships can be influenced by choices made during data collection and throughout the benchmarking process, impacting the inferred skill of land models. To avoid misrepresenting a model's true performance, it is necessary to systematically evaluate best practices when constructing functional relationship benchmarks. We developed a set of guidelines for constructing functional relationship benchmarks, considering the choice of data set, number of daily observations, temporal extent, and temporal resolution across Alaska and Canada over a 20-year period from 2001 to 2020. The temperature sensitivity of ecosystem respiration from observations, evaluated through an apparent Q 10 , is highly variable both spatially and as a result of the data processing approach applied in the benchmark formation. When benchmarking 13 models from the Warming Permafrost Model Intercomparison Project (WrPMIP), the range in inferred model skill is substantially impacted by the choices applied in constructing functional relationship benchmarks. The inferred performance of a given model is most sensitive to the number of daily observations and temporal extent, followed by choice of benchmark data set and temporal averaging. Results from this analysis can guide the development of consistent and robust functional relationships for future model evaluation studies.
A Bayesian model for multivariate discrete data using spatial and expert information with application to inferring building attributes
When modeling sparsely observed multivariate data, strong prior information elicited from experts can be used to bolster predictive accuracy and counteract sampling bias. Similarly, modeling autocorrelation in space can help make use of co-occurrence patterns present in many types of spatial data. To make use of both expert prior information and spatial structure, we propose a novel graphical model for a spatial Bayesian network developed specifically to address challenges in inferring the attributes of buildings from geographically sparse observational data. This model is implemented as the sum of a spatial multivariate Gaussian random field and a tabular conditional probability function in real-valued space prior to projection onto the probability simplex. This modeling form is especially suitable for the usage of prior information in the form of sets of atomic rules obtained from experts. To perform inference with missing data, we implement a Markov chain Monte Carlo scheme composed of alternating steps of Gibbs sampling of missing entries and Hamiltonian Monte Carlo for model parameters. A case study in building attribution is presented to highlight the advantages and limitations of this approach.
Bayesian model-data comparison incorporating theoretical uncertainties
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory’s varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.
Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models
The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.
Operator inference for non-intrusive model reduction with quadratic manifolds
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
The dedicated monitor of exotransits (DEMONEX): Seven transits of XO-4b
The DEdicated MONitor of EXotransits (DEMONEX) was a 20-inch robotic and automated telescope to monitor bright stars hosting transiting exoplanets to discover new planets and improve constraints on the properties of known transiting planetary systems. We present results for the misaligned hot Jupiter XO-4b containing seven new transits from the DEMONEX telescope, including three full and four partial transits. We combine these data with archival light curves and archival radial velocity measurements to derive the host star mass M{sub ∗}=1.293{sub −0.029}{sup +0.030} M{sub ⊙} and radius R{sub ∗}=1.554{sub −0.030}{sup +0.042} R{sub ⊙}, the planet mass M{sub P}=1.615{sub −0.099}{sup +0.10} M{sub J} and radius R{sub P}=1.317{sub −0.029}{sup +0.040} R{sub J}, and a refined ephemeris of P=4.1250687±0.0000024 days and T{sub 0}=2,4547,58.18978±0.00024 BJD{sub TDB}. We include archival Rossiter–McLaughlin measurements of XO-4 to infer the stellar spin–planetary orbit alignment of λ=−40.0{sub −7.5}{sup +8.8} degrees. We test the effects of including various detrend parameters, theoretical and empirical mass–radius relations, and Rossiter–McLaughlin models. We infer that detrending against CCD position and time or airmass can improve data quality but can have significant effects on the inferred values of many parameters—most significantly R{sub P}/R{sub ∗} and the observed central transit times T{sub C}. In the case of R{sub P}/R{sub ∗} we find that the systematic uncertainty due to detrending can be three times that of the quoted statistical uncertainties. The choice of mass–radius relation has little effect on our inferred values of the system parameters. The choice of Rossiter–McLaughlin models can have significant effects on the inferred values of vsinI{sub ∗} and the stellar spin–planet orbit angle λ.
Optimization, Inference and Learning for Advanced Networks
This piece of software aims at providing an implementation of methods to perform efficient optimization, probabilistic inference and model selection and learning for various type of networked systems. The software contains a suite of methods and functions that: 1) perform probabilistic inference and random sampling on networked models 2) select or learn networked models from data 3) solve optimization tasks with a networked structure Network models that are supported by these features include, but are not limited to, factor graphs and Markov random fields such as Ising models, Potts models, p-spins models, Gaussian random fields and restricted Boltzmann machine.
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
Here in this work we present a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.
Towards a dynamic photosynthesis model to guide yield improvement in C4 crops
Summary The most productive C4 food and biofuel crops, such as Saccharum officinarum (sugarcane), Sorghum bicolor (sorghum) and Zea mays (maize), all use NADP‐ME‐type C4 photosynthesis. Despite high productivities, these crops fall well short of the theoretical maximum solar conversion efficiency of 6%. Understanding the basis of these inefficiencies is key for bioengineering and breeding strategies to increase the sustainable productivity of these major C4 crops. Photosynthesis is studied predominantly at steady state in saturating light. In field stands of these crops light is continually changing, and often with rapid fluctuations. Although light may change in a second, the adjustment of photosynthesis may take many minutes, leading to inefficiencies. We measured the rates of CO 2 uptake and stomatal conductance of maize, sorghum and sugarcane under fluctuating light regimes. The gas exchange results were combined with a new dynamic photosynthesis model to infer the limiting factors under non‐steady‐state conditions. The dynamic photosynthesis model was developed from an existing C4 metabolic model for maize and extended to include: (i) post‐translational regulation of key photosynthetic enzymes and their temperature responses; (ii) dynamic stomatal conductance; and (iii) leaf energy balance. Testing the model outputs against measured rates of leaf CO 2 uptake and stomatal conductance in the three C4 crops indicated that Rubisco activase, the pyruvate phosphate dikinase regulatory protein and stomatal conductance are the major limitations to the efficiency of NADP‐ME‐type C4 photosynthesis during dark‐to‐high light transitions. We propose that the level of influence of these limiting factors make them targets for bioengineering the improved photosynthetic efficiency of these key crops.