A key challenge in applying MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm.

Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite element modeling environments, this can become computationally challenging-particularly for systems subjected to stochastic excitation. To address this challenge, a multi-fidelity stratified sampling scheme with adaptive machine learning metamodels is introduced for efficiently propagating uncertainties and estimating small failure probabilities. In this approach, a high-fidelity dataset generated through stratified sampling is used to train a deep learning-based metamodel, which then serves as a cost-effective and highly correlated low-fidelity model. An adaptive training scheme is proposed to balance the trade-off between approximation quality and computational demand associated with the development of the low-fidelity model. By integrating the low-fidelity outputs with additional high-fidelity results, an unbiased estimate of the strata-wise failure probabilities is obtained using a multi-fidelity Monte Carlo framework. The overall probability of failure is then computed using the total probability theorem. Application to a full-scale high-rise steel building subjected to stochastic wind excitation demonstrates that the proposed scheme can accurately estimate exceedance probability curves for nonlinear responses of interest, while achieving significant computational savings compared to single-fidelity variance reduction approaches.

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.

Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired strategies, control variate techniques, and adaptive sampling, predominantly depend on a structured hierarchy of models. However, this reliance on a model hierarchy can exacerbate variance in policy learning when the underlying models exhibit heterogeneous error distributions across the design space. To address this challenge, this work proposes a novel adaptive multi-fidelity RL framework, in which multiple heterogeneous, non-hierarchical low-fidelity models are dynamically leveraged alongside a high-fidelity model to efficiently learn a high-fidelity policy. Specifically, low-fidelity policies and their experience data are adaptively used for efficient targeted learning, guided by their alignment with the high-fidelity policy. The effectiveness of the approach is demonstrated in an octocopter design optimization problem, utilizing two low-fidelity models alongside a high-fidelity simulator. The results demonstrate that the proposed approach substantially reduces variance in policy learning, leading to improved convergence and consistent high-quality solutions relative to traditional hierarchical multi-fidelity RL methods. Moreover, the framework eliminates the need for manually tuning model usage schedules, which can otherwise introduce significant computational overhead. This positions the framework as an effective variance-reduction strategy for multi-fidelity RL, while also mitigating the computational and operational burden of manual fidelity scheduling.

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high accuracy) to the phenomena under study being often preferable. However, inferring parameters of high-fidelity models via simulation-based inference is challenging, especially when the simulator is computationally expensive. We introduce MF-NPE, a multifidelity approach to neural posterior estimation that leverages inexpensive low-fidelity simulations to infer parameters of high-fidelity simulators within a limited simulation budget. MF-NPE performs neural posterior estimation with limited high-fidelity resources by virtue of transfer learning, with the ability to prioritize individual observations using active learning. On one statistical task with analytical ground-truth and two real-world tasks, MF-NPE shows comparable performance to current approaches while requiring up to two orders of magnitude fewer high-fidelity simulations. Overall, MF-NPE opens new opportunities to perform efficient Bayesian inference on computationally expensive simulators.

Multi-fidelity Reinforcement Learning (RL) frameworks significantly enhance the efficiency of engineering design by leveraging analysis models with varying levels of accuracy and computational costs. The prevailing methodologies, characterized by transfer learning, human-inspired strategies, control variate techniques, and adaptive sampling, predominantly depend on a structured hierarchy of models. However, this reliance on a model hierarchy overlooks the heterogeneous error distributions of models across the design space, extending beyond mere fidelity levels. This work proposes ALPHA (Adaptively Learned Policy with Heterogeneous Analyses), a novel multi-fidelity RL framework to efficiently learn a high-fidelity policy by adaptively leveraging an arbitrary set of non-hierarchical, heterogeneous, low-fidelity models alongside a high-fidelity model. Specifically, low-fidelity policies and their experience data are dynamically used for efficient targeted learning, guided by their alignment with the high-fidelity policy. The effectiveness of ALPHA is demonstrated in analytical test optimization and octocopter design problems, utilizing two low-fidelity models alongside a high-fidelity one. The results highlight ALPHA's adaptive capability to dynamically utilize models across time and design space, eliminating the need for scheduling models as required in a hierarchical framework. Furthermore, the adaptive agents find more direct paths to high-performance solutions, showing superior convergence behavior compared to hierarchical agents.

We present a deep learning framework for correcting existing dynamical system models utilizing only a scarce high-fidelity data set. In many practical situations, one has a low-fidelity model that can capture the dynamics reasonably well but lacks high resolution, due to the inherent limitation of the model and the complexity of the underlying physics. When high resolution data become available, it is natural to seek model correction to improve the resolution of the model predictions. We focus on the case when the amount of high-fidelity data is so small that most of the existing data driven modeling methods cannot be applied. In this paper, we address these challenges with a model-correction method which only requires a scarce high-fidelity data set. Our method first seeks a deep neural network (DNN) model to approximate the existing low-fidelity model. By using the scarce high-fidelity data, the method then corrects the DNN model via transfer learning (TL). After TL, an improved DNN model with high prediction accuracy to the underlying dynamics is obtained. One distinct feature of the propose method is that it does not assume a specific form of the model correction terms. Instead, it offers an inherent correction to the low-fidelity model via TL. A set of numerical examples are presented to demonstrate the effectiveness of the proposed method.

Modeling thermal states for complex space missions, such as the surface exploration of airless bodies, requires high computation, whether used in ground-based analysis for spacecraft design or during onboard reasoning for autonomous operations. For example, a finite-element thermal model with hundreds of elements can take significant time to simulate, which makes it unsuitable for onboard reasoning during time-sensitive scenarios such as descent and landing, proximity operations, or in-space assembly. Further, the lack of fast and accurate thermal modeling drives thermal designs to be more conservative and leads to spacecraft with larger mass and higher power budgets. The emerging paradigm of physics-informed machine learning (PIML) presents a class of hybrid modeling architectures that address this challenge by combining simplified physics models with machine learning (ML) models resulting in models which maintain both interpretability and robustness. Such techniques enable designs with reduced mass and power through onboard thermal-state estimation and control and may lead to improved onboard handling of off-nominal states, including unplanned down-time. The PIML model or hybrid model presented here consists of a neural network which predicts reduced nodalizations (distribution and size of coarse mesh) given on-orbit thermal load conditions, and subsequently a (relatively coarse) finite-difference model operates on this mesh to predict thermal states. We compare the computational performance and accuracy of the hybrid model to a data-driven neural net model, and a high-fidelity finite-difference model of a prototype Earth-orbiting small spacecraft. The PIML based active nodalization approach provides significantly better generalization than the neural net model and coarse mesh model, while reducing computing cost by up to 1.7x compared to the high-fidelity model.

Machine learning (ML) methods, which fit to data the parameters of a given parameterized model class, have garnered significant interest as potential methods for learning surrogate models for complex engineering systems for which traditional simulation is expensive. However, in many scientific and engineering settings, generating high-fidelity data on which to train ML models is expensive, and the available budget for generating training data is limited. ML models trained on the resulting scarce high-fidelity data have high variance and are sensitive to vagaries of the training data set. We propose a new multifidelity training approach for scientific machine learning that exploits the scientific context where data of varying fidelities and costs are available; for example high-fidelity data may be generated by an expensive fully resolved physics simulation whereas lower-fidelity data may arise from a cheaper model based on simplifying assumptions. We use the multifidelity data to define new multifidelity Monte Carlo estimators for the unknown parameters of linear regression models, and provide theoretical analyses that guarantee the approach's accuracy and improved robustness to small training budgets. Numerical results verify the theoretical analysis and demonstrate that multifidelity learned models trained on scarce high-fidelity data and additional low-fidelity data achieve order-of-magnitude lower model variance than standard models trained on only high-fidelity data of comparable cost. This illustrates that in the scarce data regime, our multifidelity training strategy yields models with lower expected error than standard training approaches.

To extend the limited scope of autonomy used in prior missions for operation in distant and complex environments, there is a need to further develop and mature autonomy that jointly reasons over multiple subsystems, which we term system-level autonomy. System-level autonomy establishes situational awareness that resolves conflicting information across subsystems, which may necessitate the refinement and interconnection of the underlying spacecraft and environment onboard models. However, with a limited understanding of the assumptions and tradeoffs of modeling to arbitrary extents, designing onboard models to support system-level capabilities presents a significant challenge. In this paper, we provide a detailed analysis of the increasing levels of model fidelity for several key spacecraft subsystems, with the goal of informing future spacecraft functional- and system-level autonomy algorithms and the physics-based simulators on which they are validated. We do not argue for the adoption of a particular fidelity class of models but, instead, highlight the potential tradeoffs and opportunities associated with the use of models for onboard autonomy and in physics-based simulators at various fidelity levels. We ground our analysis in the context of deep space exploration of small bodies, an emerging frontier for autonomous spacecraft operation in space, where the choice of models employed onboard the spacecraft may determine mission success. We conduct our experiments in the Multi-Spacecraft Concept and Autonomy Tool (MuSCAT), a software suite for developing spacecraft autonomy algorithms.