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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure↗
DOE OSTI2025

Dynamic Metal–Support Interaction Dictates Cu Nanoparticle Sintering on Al 2 O 3 Surfaces

Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model based on the Perdew–Burke–Ernzerhof approximation of density functional theory for Cu nanoparticles on three Al 2 O 3 surfaces (γ-Al 2 O 3 (100), γ-Al 2 O 3 (110), and α-Al 2 O 3 (0001)). Using DP-accelerated simulations, we reveal that the nanoparticle size-mobility relationship strongly depends on the supporting surface. The diffusion of nanoparticles on the two γ-Al 2 O 3 surfaces is almost independent of the size of the nanoparticle, while the diffusion on α-Al 2 O 3 (0001) decreases rapidly with increasing size. Interestingly, nanoparticles with fewer than 55 atoms diffuse several times faster on α-Al 2 O 3 (0001) than on γ-Al 2 O 3 (100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. The diffusion on α-Al 2 O 3 (0001) is facilitated by dynamic metal–support interaction (MSI), where Al atoms move out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on γ-Al 2 O 3 (100) and on γ-Al 2 O 3 (110) is dominated by more stable and directional Cu–O bonds, consistent with the limited diffusion observed on these surfaces. Our extended MD simulations provide insight into the sintering processes, showing that the dispersity of the nanoparticles strongly influences the coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu 13 nanoparticles on α-Al 2 O 3 (0001) can occur in a short time (10 ns) at 800 K even with an initial internanoparticle distance increased to 3 nm, while the coalescence on the two γ-Al 2 O 3 surfaces are inhibited significantly by increasing the initial internanoparticle distance. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Experimental observation of localized interfacial phonon modes

Interfaces impede heat flow in micro/nanostructured systems. Conventional theories for interfacial thermal transport were derived based on bulk phonon properties of the materials making up the interface without explicitly considering the atomistic interfacial details, which are found critical to correctly describing thermal boundary conductance. Recent theoretical studies predicted the existence of localized phonon modes at the interface which can play an important role in understanding interfacial thermal transport. However, experimental validation is still lacking. Through a combination of Raman spectroscopy and high-energy-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope, we report the experimental observation of localized interfacial phonon modes at ~12 THz at a high-quality epitaxial Si-Ge interface. These modes are further confirmed using molecular dynamics simulations with a high-fidelity neural network interatomic potential, which also yield thermal boundary conductance agreeing well with that measured in time-domain thermoreflectance experiments. Simulations find that the interfacial phonon modes have an obvious contribution to the total thermal boundary conductance. Our findings significantly contribute to the understanding of interfacial thermal transport physics and have impact on engineering thermal boundary conductance at interfaces in applications such as electronics thermal management and thermoelectric energy conversion.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fast uncertainty estimates in deep learning interatomic potentials

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and material properties. A common short-coming shared by current approaches, however, is that neural networks only give point estimates of their predictions and do not come with predictive uncertainties associated with these estimates. Existing uncertainty quantification efforts have primarily leveraged the standard deviation of predictions across an ensemble of independently trained neural networks. This incurs a large computational overhead in both training and prediction, resulting in order-of-magnitude more expensive predictions. Here, we propose a method to estimate the predictive uncertainty based on a single neural network without the need for an ensemble. This allows us to obtain uncertainty estimates with virtually no additional computational overhead over standard training and inference. We demonstrate that the quality of the uncertainty estimates matches those obtained from deep ensembles. We further examine the uncertainty estimates of our methods and deep ensembles across the configuration space of our test system and compare the uncertainties to the potential energy surface. Finally, we study the efficacy of the method in an active learning setting and find the results to match an ensemble-based strategy at order-of-magnitude reduced computational cost.

Chemistry↗
DOE OSTI2024

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids—including the density response, surface tension and size-dependent cavitation free energies—for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Modeling the Behavior of Complex Aqueous Electrolytes Using Machine Learning Interatomic Potentials: The Case of Sodium Sulfate

Understanding the structure and thermodynamics of solvated ions is essential for advancing applications in electrochemistry, water treatment, and energy storage. While ab initio molecular dynamics methods are highly accurate, they are limited by short accessible time and length scales whereas classical force fields struggle with accuracy. Herein, we explore the structure and thermodynamics of complex monovalent-divalent ion pairs using Na 2 SO 4 (aq) as a case study by applying a machine learning interatomic potential (MLIP) trained on density functional theory (DFT) data. Our MLIP-based approach reproduces key bulk properties such as density and radial distribution functions of water. We provide the hydration structure of the sodium and sulfate ions in the 0.1–2 M concentration range and the one-dimensional and two-dimensional potentials of mean force for the sodium–sulfate ion pairing at the low concentration limit (0.1 M), which are inaccessible to DFT. At low concentrations, the sulfate ion is strongly solvated, leading to the stabilization of solvent-separated ion pairs over contact ion pairs. Minimum energy pathway analysis revealed that coordinating two sodium ions with a sulfate ion is a multistep process whereby the sodium ions coordinate to the sulfate ion sequentially. Finally, we demonstrate that MLIPs allow the study of solvated ions beyond simple monovalent pairs with DFT-level accuracy in their low concentration limit (0.1 M) via statistically converged properties from ns-long simulations.

anions↗
DOE OSTI2024

A Molecular View of Methane Activation on Ni(111) through Enhanced Sampling and Machine Learning

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a dataset constructed via ab initio molecular dynamics (AIMD) simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that by incorporating collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting DFT-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH 4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression towards the transition state involves an CH 4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C–H bond. Furthermore, this leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Role of Wadsley Defects and Cation Disorder to Enhance MoNb 12 O 33 Diffusion

Wadsley-Roth (WR) niobates have emerged as high-rate anode materials that can combine rapid ionic diffusion with good electronic conductivity. WR compounds have been defect-enhanced by limited annealing, however, such materials often contain multiple types of defects. In particular, both Wadsley defects (variable block size) and transition metal disorder have the potential to modify transport rates, however the corresponding effects are not well understood mechanistically. Here, MoNb 12 O 33 (MNO) was calcined at two different temperatures to compare a defect-rich condition (MNO-800) with a proximal order-rich condition (MNO-900) as assessed through XRD, XANES, EXAFS, and STEM characterizations. Galvanostatically cycled lithium half cells of MNO-800 exhibited additional capacity (307 mAhg −1 at 0.1C, 4.66% higher) and improved high-rate capacity of 200 mAhg −1 at 10C. ICI-based overpotential analysis identified solid state diffusion as the dominant rate limiting process where MNO-800 correspondingly exhibited ∼3X faster capacity-weighted diffusivity. A machine-learning interatomic potential was trained to density functional theory and then applied with molecular dynamics (MLIP-MD) to examine the possible roles of Wadsley defects and transition metal disorder. For both defect-types, Li was found to populate and activate fast diffusion paths from window sites at lower extents of lithiation as compared to the order-rich model.

defect↗
DOE OSTI2026

Protonation Dynamics of Confined Ethanol–Water Mixtures in H-ZSM-5 from Machine Learning-Driven Metadynamics

Zeolites are indispensable heterogeneous catalysts in industrial chemical processes, valued for their strong Brønsted acidity, well-defined microporous frameworks, and tunable pore structures. Their catalytic activity arises primarily from Brønsted acid sites (BAS), typically present as bridging hydroxyl groups (Si–OH–Al). Under aqueous reaction conditions, these protons interact dynamically with water and alcohol molecules, leading to complex solvation and protonation behavior within confined pores. In this study, we investigate the protonation equilibrium occurring between ethanol and water at the BAS of acidic zeolites under varying hydration levels, i.e., C2H5OH–(H2O)n, n=1–4. Local structure was analyzed through an adaptive-learning global optimization algorithm, while enhanced sampling molecular dynamics simulations with Well-Tempered Metadynamics (WMetaD) and machine learning interatomic potentials (MLPs) provide free-energy surfaces (FES) at variable hydration levels. The results reveal a strong dependence of proton localization on the degree of hydration. At low hydration (1 water molecule), the proton resides predominantly on ethanol; with 2 water molecules, it shifts toward water, and at higher hydration (3 or more water molecules), it becomes extensively delocalized over the water cluster. These findings underscore the critical role of solvation in modulating acid site behavior and suggest that a minimum of three water molecules is necessary to fully stabilize the proton on water within the zeolite framework. This solvation threshold has significant implications for catalytic processes, particularly in biomass conversion reactions where alcohol protonation is a key step in dehydration mechanisms.

machine learning↗
DOE OSTI2022

Benchmarking structural evolution methods for training of machine learned interatomic potentials

When creating training data for machine-learned interatomic potentials (MLIPs), it is common to create initial structures and evolve them using molecular dynamics (MD) to sample a larger configuration space. Here, we benchmark two other modalities of evolving structures, contour exploration (CE) and dimer-method (DM) searches against MD for their ability to produce diverse and robust density functional theory training data sets for MLIPs. We also discuss the generation of initial structures which are either from known structures or from random structures in detail to further formalize the structure-sourcing processes in the future. The polymorph-rich zirconium-oxygen composition space is used as a rigorous benchmark system for comparing the performance of MLIPs trained on structures generated from these structural evolution methods. Using Behler–Parrinello neural networks as our MLIP models, we find that CE and the DM searches are generally superior to MD in terms of spatial descriptor diversity and statistical accuracy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

A theoretical study of solid solution strengthening in the refractory medium entropy alloy Nb 45 Ta 25 Ti 15 Hf 15

The refractory medium-entropy alloy (RMEA) Nb 45 Ta 25 Ti 15 Hf 15 exhibits exceptional tensile ductility and fracture toughness at ambient temperature, but its engineering applications are limited by a lack of high temperature strength. Using a machine-learning interatomic potential (MLIP) with near-density functional theory (DFT) accuracy, we conducted molecular dynamics (MD) and statics simulations of the behavior of dislocations with both screw and edge characters. We also analyze experimentally measured yield strengths using the Rao-Suzuki model and the Maresca-Curtin model modified to include a temperature-dependent shear modulus and a bulk modulus-dependent misfit volume, thereby uncovering the mechanisms underlying the yielding of this RMEA. Compared with the published experimental yield strength, the models parameterized by the MLIP effectively reproduce the experimental results over a wide temperature range. The models and MD simulations indicate that yielding is governed by screw dislocations, with dipole dragging as the dominant mechanism. In MD simulations, we observed a potential softening mechanism not considered by the Rao-Suzuki screw model: slow migration of interstitial jogs along the dislocation core, which could lead to the annihilation of vacancy and interstitial jog pairs by their combination.

BCC complex concentrated alloys↗
DOE OSTI2021

Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order

Abstract Refractory high-entropy alloys (RHEAs) are designed for high elevated-temperature strength, with both edge and screw dislocations playing an important role for plastic deformation. However, they can also display a significant energetic driving force for chemical short-range ordering (SRO). Here, we investigate mechanisms underlying the mobilities of screw and edge dislocations in the body-centered cubic MoNbTaW RHEA over a wide temperature range using extensive molecular dynamics simulations based on a highly-accurate machine-learning interatomic potential. Further, we specifically evaluate how these mechanisms are affected by the presence of SRO. The mobility of edge dislocations is found to be enhanced by the presence of SRO, whereas the rate of double-kink nucleation in the motion of screw dislocations is reduced, although this influence of SRO appears to be attenuated at increasing temperature. Independent of the presence of SRO, a cross-slip locking mechanism is observed for the motion of screws, which provides for extra strengthening for refractory high-entropy alloy system.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Active and Transfer Learning of High-Dimensional Neural Network Potentials for Transition Metals

Classical molecular dynamics (MD) simulations represent a very popular and powerful tool for materials modeling and design. The predictive power of MD hinges on the ability of the interatomic potential to capture the underlying physics and chemistry. There have been decades of seminal work on developing interatomic potentials, albeit with a focus predominantly on capturing the properties of bulk materials. Such physics-based models, while extensively deployed for predicting the dynamics and properties of nanoscale systems over the past two decades, tend to perform poorly in predicting nanoscale potential energy surfaces (PESs) when compared to high-fidelity first-principles calculations. These limitations stem from the lack of flexibility in such models, which rely on a predefined functional form. Machine learning (ML) models and approaches have emerged as a viable alternative to capture the diverse size-dependent cluster geometries, nanoscale dynamics, and the complex nanoscale PESs, without sacrificing the bulk properties. Here, in this study, we introduce an ML workflow that combines transfer and active learning strategies to develop high-dimensional neural networks (NNs) for capturing the cluster and bulk properties for several different transition metals with applications in catalysis, microelectronics, and energy storage, to name a few. Our NN first learns the bulk PES from the high-quality physics-based models in literature and subsequently augments this learning via retraining with a higher-fidelity first-principles training data set to concurrently capture both the nanoscale and bulk PES. Our workflow departs from status-quo in its ability to learn from a sparsely sampled data set that nonetheless covers a diverse range of cluster configurations from near-equilibrium to highly nonequilibrium as well as learning strategies that iteratively improve the fingerprinting depending on model fidelity. All the developed models are rigorously tested against an extensive first-principles data set of energies and forces of cluster configurations as well as several properties of bulk configurations for 10 different transition metals. Our approach is material agnostic and provides a methodology to transfer and build upon the learnings from decades of seminal work in molecular simulations on to a new generation of ML-trained potentials to accelerate materials discovery and design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Electron-irradiation induced creep in amorphous alloys

Electron-irradiation induced creep rates in amorphous alloys, a-SiO2, Fe79B16Si5, Cu60Ta40, and Cu50Ti50, were measured at room temperature using a miniaturized beam-bending apparatus within a transmission electron microscope operated at 200 keV. The creep rates of these amorphous samples increased nearly linearly with both e-beam current density and applied stress, while a reference crystalline (c-)SiO2 sample failed to creep under the same conditions. The irradiation induced creep compliance of a-SiO2 was ~ 15 times larger than that of Fe79B16Si5 and over 1,000 times larger than that of the two Cu alloys. Molecular dynamics computer simulations were employed to simulate electron irradiation induced creep using interatomic potentials representing amorphous Cu75Zr25, Ni80P20, and SiO2 as model systems. The irradiation induced creep compliances calculated for Cu75Zr25 during 200 keV electron irradiation provided good quantitative agreement with the two Cu-based alloys, but that for a-SiO2 was ~ 180 times too small. These results indicate that unlike neutron or ion-beam induced creep in a-SiO2, creep under electron irradiation is dominated by the effects of ionization owing largely to the far higher ratio of electronic stopping to nuclear stopping for electrons than for ions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Development of interatomic potential and effect of ordering on defect properties in CrMnV

Developing materials that can withstand extreme environments, such as high radiation doses and elevated temperatures, is crucial for next-generation particle accelerators, including the 2.4 MW Long-Baseline Neutrino Facility. High-Entropy Alloys have emerged as promising candidates for beam window materials due to their superior mechanical strength, corrosion resistance, and radiation tolerance. In this study, we focus on the Cr–Mn–V alloy system, developing and employing machine-learning interatomic potentials (MLIPs) to investigate the formation of an ordered phase and its influence on defect properties. Using hybrid Monte Carlo-Molecular Dynamics simulations, we observe the formation of a B2-ordered phase at lower temperatures, consistent with Density Functional Theory (DFT) predictions. Ordered structures display a bimodal distribution of migration energies and reduced mean square displacement values, indicating suppressed vacancy diffusion. Our results also show that the migration energy barrier varies based on the atomic species, with Mn and V exhibiting the highest and lowest average barriers, respectively. These findings suggest that atomic ordering inhibits defect mobility, potentially enhancing the radiation resistance of CrMnV alloys. The validated MLIP provides a reliable framework for simulations that are faster than traditional DFT while maintaining the accuracy required to study defect and ordering properties.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Bayesian Calibration Framework with Embedded Model Error for Model Diagnostics

We study the utility and performance of a Bayesian model error embedding construction in the context of molecular dynamics modeling of metallic alloys, where we embed model error terms in existing interatomic potential model parameters. To alleviate the computational burden of this approach, we propose a framework combining likelihood approximation and Gaussian process surrogates. Here we leverage sparse Gaussian process techniques to construct a hierarchy of increasingly accurate but more expensive surrogate models. This hierarchy is then exploited by multilevel Markov chain Monte Carlo methods to efficiently sample from the target posterior distribution. We illustrate the utility of this approach by calibrating an interatomic potential model for a family of gold-copper alloys. In particular, this case study highlights effective means for dealing with computational challenges with Bayesian model error embedding in large-scale physical models, and the utility of embedded model error for model diagnostics.

Bayesian inference↗