Solving inverse problems in process-structure-property linkage with Gaussian process regression.
Abstract not provided.
Tran, Anh↗
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Multi-fidelity modeling to predict the rheological properties of a suspension of fibers using neural networks and Gaussian processes
Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications. There are multiple factors, such as fiber aspect ratio and volume fraction, that play a significant role in altering the rheological behavior of suspensions. Three-dimensional (3D) numerical simulations of coupled differential equations of the suspension of fibers are computationally expensive and time-consuming. Machine learning algorithms can be trained on the available data and make predictions for the cases where no numerical data are available. However, some widely used machine learning surrogates, such as neural networks, require a relatively large training dataset to produce accurate predictions. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified constitutive equations, can pave the way for more accurate predictions. Here, we focus on neural networks and the Gaussian processes with two levels of fidelity, i.e., high and low fidelity networks, to predict the steady-state rheological properties, and compare them to the single-fidelity network. High-fidelity data are obtained from direct numerical simulations based on an immersed boundary method to couple the fluid and solid motion. The low-fidelity data are produced by using constitutive equations. Multiple neural networks and the Gaussian process structures are used for the hyperparameter tuning purpose. Results indicate that with the best choice of hyperparameters, both the multi-fidelity Gaussian processes and neural networks are capable of making predictions with a high level of accuracy with neural networks demonstrating marginally better performance.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Bayesian Active Learning for Scanning Probe Microscopy: From Gaussian Processes to Hypothesis Learning
Recent progress in machine learning methods and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs) have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. Here, the discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods and can be particularly impactful for destructive or irreversible measurements.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Hypothesis Learning in Automated Experiment: Application to Combinatorial Materials Libraries
Machine learning is rapidly becoming an integral part of experimental physical discovery via automated and high-throughput synthesis, and active experiments in scattering and electron/probe microscopy. This, in turn, necessitates the development of active learning methods capable of exploring relevant parameter spaces with the smallest number of steps. In this work, an active learning approach based on conavigation of the hypothesis and experimental spaces is introduced. This is realized by combining the structured Gaussian processes containing probabilistic models of the possible system's behaviors (hypotheses) with reinforcement learning policy refinement (discovery). This approach closely resembles classical human-driven physical discovery, when several alternative hypotheses realized via models with adjustable parameters are tested during an experiment. This approach is demonstrated for exploring concentration-induced phase transitions in combinatorial libraries of Sm-doped BiFeO 3 using piezoresponse force microscopy, but it is straightforward to extend it to higher-dimensional parameter spaces and more complex physical problems once the experimental workflow and hypothesis generation are available.
36 MATERIALS SCIENCE↗
Physics-driven discovery and bandgap engineering of hybrid perovskites
Discovery of physical models of binary compositions using structured Gaussian Process (sGP) with physics-informed mean functions, optimizing materials post-discovery to enhance design and application efficiency.
Sanchez, Sheryl L.↗
Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data
We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.
Chemical structure↗
Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian process-based exploration–exploitation
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds remain undiscovered. Here, we demonstrate that a combination of exploration and exploration–exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore the parameter space of more complex off-lattice and dynamic models.
42 ENGINEERING↗
Short-Term Load Forecasting Considering EV Charging Loads with Prediction Interval Evaluation
Short-term load forecasting plays a critical role in power system planning and operation. Along with the electrification of various loads, electricity demands are becoming increasingly hard to predict. Notably, the recent rise in electric vehicles (EVs) has further contributed to this unpredictability. To address this issue, this paper proposes a probabilistic load forecasting strategy utilizing Gaussian process regression, structured in a day-ahead manner. While many works focus on deterministic prediction, probabilistic forecasting offers additional insights into variability and uncertainty, enabling more flexible and reliable operation for power systems. To enhance the accuracy of the load forecasting model, the inputs include features related to EV charging habits as well as commonly used weather information. The load forecasting results are evaluated using various metrics, including conventional ones that assess the accuracy of point forecasts, as well as additional metrics that test the reliability of prediction intervals. The proposed load forecasting method is finally tested on real residential power consumption data and EV charging data sampled from real-world sources. The results prove that the new features can greatly improve the performance of the load forecasting method.
electrical vehicle↗
Bayesian Learning of Adatom Interactions from Atomically Resolved Imaging Data
Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. In this work, we develop a workflow based on a machine-learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization
Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. Here, the associated notebooks allow to reproduce the reported analyses and apply them to other systems.
97 MATHEMATICS AND COMPUTING↗
Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.
Science & Technology - Other Topics↗
Featureless adaptive optimization accelerates functional electronic materials design
Electronic materials that exhibit phase transitions between metastable states (e.g., metal-insulator transition materials with abrupt electrical resistivity transformations) are challenging to decode. For these materials, conventional machine learning methods display limited predictive capability due to data scarcity and the absence of features that impede model training. In this article, we demonstrate a discovery strategy based on multi-objective Bayesian optimization to directly circumvent these bottlenecks by utilizing latent variable Gaussian processes combined with high-fidelity electronic structure calculations for validation in the chalcogenide lacunar spinel family. We directly and simultaneously learn phase stability and bandgap tunability from chemical composition alone to efficiently discover all superior compositions on the design Pareto front. Previously unidentified electronic transitions also emerge from our featureless adaptive optimization engine. Our methodology readily generalizes to optimization of multiple properties, enabling co-design of complex multifunctional materials, especially where prior data is sparse.
36 MATERIALS SCIENCE↗
Quantifying correlated truncation errors in effective field theory
Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Imaging mechanism for hyperspectral scanning probe microscopy via Gaussian process modelling
We investigate the ability to reconstruct and derive spatial structure from sparsely sampled 3D piezoresponse force microcopy data, captured using the band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for weakly informative priors, GP methods allow unambiguous determination of the characteristic length scales of the imaging process both in spatial and frequency domains. We further show that BE data set tends to be oversampled in the spatial domains, with ~30% of original data set sufficient for high-quality reconstruction, potentially enabling faster BE imaging. At the same time, reliable reconstruction along the frequency domain requires the resonance peak to be within the measured band. This behavior suggests the optimal strategy for the BE imaging on unknown samples. Finally, we discuss how GP can be used for automated experimentation in SPM, by combining GP regression with non-rectangular scans.
47 OTHER INSTRUMENTATION↗
Physics makes the difference: Bayesian optimization and active learning via augmented Gaussian process
Abstract Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization (BO) strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected system’s behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of a standard univariate test function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the BO framework.
42 ENGINEERING↗
Machine learning with bond information for local structure optimizations in surface science
Local optimization of adsorption systems inherently involves different scales: within the substrate, within the molecule, and between the molecule and the substrate. In this work, we show how the explicit modeling of different characteristics of the bonds in these systems improves the performance of machine learning methods for optimization. Furthermore, we introduce an anisotropic kernel in the Gaussian process regression framework that guides the search for the local minimum, and we show its overall good performance across different types of atomic systems. The method shows a speed-up of up to a factor of two compared with the fastest standard optimization methods on adsorption systems. Additionally, we show that a limited memory approach is not only beneficial in terms of overall computational resources but can also result in a further reduction of energy and force calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion
In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗