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Conclusions: certain data-driven models do implicitly what physics simulations do explicitly; theoretical underpinnings in Koopman theory, delay-coordinate embeddings, and Mori-Zwanzig formalism; best approach for given system with finite data an open question; physics-informed machine learning (PIML) emerging framework for combining explicit and implicit modeling.
Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g.,having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound [1]. However, the approach in [1] requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES)combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.
Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.
Geomagnetic disturbances can greatly disrupt the power grid operation. This is caused by low-frequency changes in the earth’s magnetic field, which upon interaction with the deep earth conductivity induces a changing electric field at the earth’s surface. This in turn induces quasi-direct currents which have the potential to cause protective devices to operate, widespread damage to high-voltage transformers, or voltage collapse due to induced reactive power losses. While these impacts have been known since the 1940s, only recently have standards for GMD response been implemented. Because these standards are heavily based on models, it is important to understand when it is appropriate to make certain modeling assumptions. In this work, implicit modeling uncertainty is quantified for the purpose of enhanced decision making for disturbance impact mitigation. Considering electromagnetic models, modeling assumptions of non-uniform grounding, imbalanced operation, transformer saturation, and geomagnetically induced currents, voltage estimation values are analyzed. Statistical characteristics of modeling uncertainty are obtained by analysis of synthetically generated data. Results statistically characterize geomagnetic disturbances modeling uncertainty, providing an important tool for impact mitigation.
A design procedure for determining the control gains of a discrete-time ('digital') control system is presented. The method is separable into four distinct steps: (1) the definition of closed-loop response criteria, (2) the choice of a discrete-time model which provides the desired response, (3) the determination of control gains which implicitly force the actual system to follow the desired response, and (4) the reduction of the measurement state by the introduction of an 'observer' (a form of integral-differential compensation). It is shown that a single desired response does not completely define the 'ideal' system. The response criterion generally leaves some parameters of the model unspecified, allowing two courses for improving the model: (1) definition of additional response criteria, or (2) redefinition of the discrete-time model for improved implicit model-following with the actual closed-loop system.
A transformation in the s-plane is described which has utility in implicit model-following optimal control design application and in estimation or parameter identification problems. The objective of the transformation is, for the control problem, to achieve an unstable closed-loop system, and, for the estimation problem, to alleviate algorithm convergence problems that may arise in identifying unstable systems. For the control problem, the transformation is a shift along the real (sigma) axis of the plant and model poles and zeros. This transformation is shown to be equivalent to a modified performance index but offers the advantage of compatibility with existing optimal control solution algorithms. For the estimation problem, the data are multiplied by an exponential function and the assumed measurement and process noise covariances are appropriately modified. Examples of both control and estimation applications are presented.
An extended model-following control-synthesis method, including loop-transfer recovery, is presented and applied to synthesize control laws for integrated flight and propulsion control (IFPC). The vehicle considered is representative of an unstable modern fighter aircraft; with a two-dimensional thrust-vectoring and thrust-reversing nozzle. The linearized design model includes both airframe and engine dynamics. A model-following formulation of the LQR problem is extended to handle this hybrid problem. Compensators are then obtained to realize an output-feedback control law, by using a loop-transfer-recovery procedure. The airframe and engine responses are decoupled, and perfect airframe response following is obtained. The loop transfers also reveal good stability robustness and reasonable loop cross-over frequencies that would not lead to excessive actuation requirements.
Implicit solvent models are a computationally efficient method of representing solid/liquid interfaces prevalent in electrocatalysis, energy storage, and materials science. However, electronic structure changes induced at the metallic surface by the dielectric continuum are not fully understood. To address this, we perform DFT calculations for the Pt(111)/water interface, in order to compare Poisson–Boltzmann continuum solvation methods with ab initio molecular dynamics (AIMD) simulations of explicit solvent. We show that the implicit solvent cavity can be parametrized in terms of the electric dipole moment change at the equilibrated explicit Pt/water interface to obtain the potential of zero charge (PZC). We also compare the accuracy of aqueous enthalpies of adsorption of phenol on Pt(111) using geometry and charge density based dielectric cavitation methods. The ability to parametrize the cavity according to individual atoms, as afforded in the geometry based approach, is key to obtaining accurate enthalpy changes of adsorption under aqueous conditions. Additionally, we show that the electronic structure changes induced by explicit solvent and our proposed implicit solvent parametrization scheme yield comparable density difference profiles and d-band projected density of states. We therefore demonstrate the capability of implicit solvent approaches to capture both the energetics of adsorption processes and the main electronic effects of aqueous solvent on the metallic surface. Therefore, this work provides a scheme for computationally efficient simulations of interfacial processes for applications in areas such as heterogeneous catalysis and electrochemistry.
Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT)-an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecular solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions and thus provides a convenient framework to investigate the assumptions in implicit solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit solvent models for polyglycine and polyalanine solutes covering a range of chain lengths and conformations. The hydration free energies or the differences in hydration free energies between conformers obtained from the implicit solvent models do not agree with explicit solvent results, with the deviations being largest for the group additive EEF1 and ABSINTH models. GB/SA does better in capturing the qualitative trends seen in explicit solvent results. Finally, analysis founded on QCT reveals the critical importance of the cooperativity of hydration that is inherent in the hydrophilic and hydrophobic contributions to hydration-physics that is not well captured in additive models but somewhat better accounted for by means of a dielectric in the GB/SA approach.
An implicit model-following flight controller is proposed. This controller is relatively simple in concept: it provides an input/output relationship that is approximately that of any selected second order system; it provides good gust alleviation; and it is self-trimming. The flight controller was applied to all axes of a comprehensive mathematical model of a lift-fan V/STOL transport. Power management controls and displays were designed to match the various modes of control provided by the flight controller. A piloted simulation was performed using a six degree of freedom simulator. The fixed-operating-point handling qualities throughout the powered lift flight envelope received pilot ratings of 3-1/2 or better. Approaches and vertical landings in IFR zero-zero conditions received pilot ratings varying from 2-1/2 to 4 depending on the type of approach and weather conditions.
Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.
Machine-learning prediction algorithms such as AlphaFold and RoseTTAFold can create remarkably accurate protein models, but these models usually have some regions that are predicted with low confidence or poor accuracy. We hypothesized that by implicitly including new experimental information such as a density map, a greater portion of a model could be predicted accurately, and that this might synergistically improve parts of the model that were not fully addressed by either machine learning or experiment alone. An iterative procedure was developed in which AlphaFold models are automatically rebuilt on the basis of experimental density maps and the rebuilt models are used as templates in new AlphaFold predictions. We show that including experimental information improves prediction beyond the improvement obtained with simple rebuilding guided by the experimental data. This procedure for AlphaFold modeling with density has been incorporated into an automated procedure for interpretation of crystallographic and electron cryo-microscopy maps.
The main goal of this project is to develop a multi-scale modeling approach that connects micron-scale phase-field models and atomic-scale density functional theory (DFT)-based simulations via parameter- and relationship-passing in order to predict Li-metal dendrite morphology evolution, in both liquid and solid electrolytes. The key hypothesis of the DFT-informed phase-field multiscale modeling approach is that it can capture the electrochemical-mechanical driving forces and incorporate the roles of nano-meter-thin solid electrolyte interphase (SEI) in liquid electrolytes as well as of the microstructures of micro-meter-thick solid electrolytes (SEs) for all-solid-state batteries. In this project, we have formulated and implemented phase-field models to incorporate the electrochemical driving forces in liquid electrolytes and then incorporate mechanical driving forces to simulate dendrite growth in solid electrolytes with resolved microstructures. We have implemented two treatments for the SEI: an explicit model to include the microstructure of the SE or SEI in the phase field model and an implicit model to simulate the impact of nano-meter thick SEI in liquid electrolytes by varying the electrode/electrolyte interfacial properties. The key interfacial properties, including the electronic and ionic transport properties, the charge transfer reaction kinetics, and mechanical properties, were computed by DFT-based calculations. At the DFT-based model, one key advancement is to directly predict the charge transfer reaction kinetics at a complex Li/SEI/electrolyte interface by linking DFT with density functional tight binding (DFTB) calculations. As the main accomplishments, we have demonstrated two successful predictions in both solid electrolyte and liquid electrolyte based on this multiscale approach. The predicted intergranular Li dendrite growth in LLZO revealed the importance of trapped electrons at internal interfaces in the microstructure of LLZO. The predicted electroplating morphology of mossy Li and faceted Mg agreed well with experiments. The insights provided by the multiscale model and the model enabled electrolyte and SEI design will accelerate the development of Li-metal electrode for high energy density batteries, that meet DOE’s target on cell density (>350 Wh/kg) and cost below $100/kWhuse for EV applications.
Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.
Prediction of 2D cross-section and full 3D geometry for stacked weld beads is critical for the outcome of wire-arc directed energy deposition (DED) parts; however, most additive path planning software packages model beads as extrusions of a rectangle. Weld beads are not rectangular, and the resulting shape is dependent upon physics effects at the moment of deposition. Physics phenomena such as the geometry of the underlying surface, the heat input of the welding mode, and the direction of gravity contribute to bead shape. Here, this paper presents a novel implicit modeling method that discretizes a 2D area or 3D volume of space into pixels or voxels and constructs fields based on these physics phenomena. The fields are combined using a weighting scheme trained on 3D scan measurements of welds and wire-arc DED prints. Pixels or voxels are added until the known amount of deposited volume has been achieved. Thereby, a strong conservation of mass principle is applied to the process. Utilizing machine learning techniques, the present model can be trained on a database of scans allowing for the representation of a wide variety of prints. Results show that this method can produce predictions with realistic bead morphology and sub-millimeter form error.
This errata is to correct the acknowledgment in the original published article. G.B. (partial support), V.-A.G., M.-T.N., and R.R. were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. Computer resources were provided by Research Computing at Pacific Northwest National Laboratory and the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. G.B. acknowledges the EPSRC for partial support in PhD funding. The authors acknowledge the use of the IRIDIS High Performance Computing Facility (IRIDIS 5) and associated support services at the University of Southampton in the completion of this work. We are grateful to the UK Materials and Molecular Modeling Hub (Thomas HPC) for computational resources, which is partially funded by EPSRC (EP/P020194/1).
Abstract not provided.
An explicit model for cloud microphysics was developed for application to the problem of co-condensation/vaporization of HCl and H2O in the presence of Al2O3 particulate nuclei. Validity of the explicit model relative to the implicit model, which has been customarily applied to atmospheric cloud studies, was demonstrated by parallel computations of H2O condensation upon (NH4)2 SO4 nuclei. A mesoscale predictive model designed to account for the impact of wet processes on atmospheric dynamics is also under development. Input data specifying the equilibrium state of HC1 and H2O vapors in contact with aqueous HC1 solutions were found to be limited, particularly in respect to temperature range.