We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, non-autonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed of a sequence of local parametric dynamical systems. We approximate these parametric systems using two complementary approaches. First, we employ the DRIPS (dimension reduction and interpolation in parameter space) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ FML (Flow Map Learning), a deep neural network approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of non-autonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

Reconstruction of 3D erythrocyte or red blood cell (RBC) morphology from partial observations, such as microscope images, is essential for understanding the physiology of RBC aging and the pathology of various RBC disorders. In this study, we propose a multi-fidelity neural network (MFNN) approach to fuse high-fidelity cross-sections of an RBC, with a morphologically similar low-fidelity reference 3D RBC shape to recover its full 3D surface. The MFNN predictor combines a convolutional neural network trained on low-fidelity reference RBC data with a feedforward neural network that captures nonlinear morphological correlations, and augments training with surface area and volume constraints for regularization in the low-fidelity branch. This approach is theoretically grounded by a topological homeomorphism between a sphere and 3D RBC surfaces, with training data generated by dissipative particle dynamics simulations of stomatocyte-discocyte-echinocyte transformation. Benchmarking across diverse RBC shapes observed in normal and aged populations, our results show that the MFNN predictor can reconstruct complex RBC morphologies with over 95% coordinate accuracy when provided with at least two orthogonal cross-sections. It is observed that informative oblique cross-sections intersecting spicule tips of echinocytes improve both local and global feature reconstruction, highlighting the value of feature-aware sampling. Our study further evaluates the influence of sampling strategies, shape dissimilarity, and noise, showing enhanced robustness under physically constrained training. Altogether, these results demonstrate the capability of MFNN to reconstruct the 3D shape of normal and aged RBCs from partial cross-sections as observed in conventional microscope images, which could facilitate the quantitative analysis of RBC morphological parameters in normal and disease-related RBC samples.

Machine learning force fields (MLFFs), which employ neural networks to map atomic structures to system energies, effectively combine the high accuracy of first-principles calculation with the computational efficiency of empirical force fields. They are widely used in computational materials simulations. However, the development and application of MLFFs for lithium-ion battery cathode materials remain relatively limited. This is primarily due to the complex electronic structure characteristics of cathode materials and the resulting scarcity of high-quality computational datasets available for force field training. In this work, we develop a multi-fidelity machine learning force field framework to enhance the data efficiency of computational results, which can simultaneously utilize both low-fidelity non-magnetic and high-fidelity magnetic computational datasets of cathode materials for training. Tests conducted on the lithium manganese iron phosphate (LMFP) cathode material system demonstrate the effectiveness of this multi-fidelity approach. This work helps to achieve high-accuracy MLFF training for cathode materials at a lower training dataset cost, and offers new perspectives for applying MLFFs to computational simulations of cathode materials.

Many reinforcement learning (RL) algorithms require large amounts of data, prohibiting their use in applications where frequent interactions with operational systems are infeasible, or high-fidelity simulations are expensive or unavailable. Meanwhile, low-fidelity simulators--such as reduced-order models, heuristic reward functions, or generative world models--can cheaply provide useful data for RL training, even if they are too coarse for direct sim-to-real transfer. We propose multi-fidelity policy gradients (MFPGs), an RL framework that mixes a small amount of data from the target environment with a large volume of low-fidelity simulation data to form unbiased, reduced-variance estimators (control variates) for on-policy policy gradients. We instantiate the framework by developing multi-fidelity variants of two policy gradient algorithms: REINFORCE and proximal policy optimization. Experimental results across a suite of simulated robotics benchmark problems demonstrate that when target-environment samples are limited, MFPG achieves up to 3.9x higher reward and improves training stability when compared to baselines that only use high-fidelity data. Moreover, even when the baselines are given more high-fidelity samples--up to 10x as many interactions with the target environment--MFPG continues to match or outperform them. Finally, we observe that MFPG is capable of training effective policies even when the low-fidelity environment is drastically different from the target environment. MFPG thus not only offers a novel paradigm for efficient sim-to-real transfer but also provides a principled approach to managing the trade-off between policy performance and data collection costs.

As machine learning (ML) techniques gain prominence in power system research, validating these methods' effectiveness under real-world conditions requires real-time hardware-in-the-loop (HIL) simulations. HIL simulation platforms enable the integration of computational models with physical devices, allowing rigorous testing across diverse scenarios critical to system resilience and reliability. In this study, we develop a SafePowerGraph-HIL framework that utilizes HIL simulations on the IEEE 9-bus system, modeled in Hypersim, to generate high-fidelity data, which is then transmitted in real-time via SCADA to an AWS cloud database before being input into a Heterogeneous Graph Neural Network (HGNN) model designed for power system state estimation and dynamic analysis. By leveraging Hypersim's capabilities, we simulate complex grid interactions, providing a robust dataset that captures critical parameters for HGNN training. The trained HGNN is subsequently validated using newly generated data under varied system conditions, demonstrating accuracy and robustness in predicting power system states. The results underscore the potential of integrating HIL with advanced neural network architectures to enhance the real-time operational capabilities of power systems. This approach represents a significant advancement toward the development of intelligent, adaptive control strategies that support the robustness and resilience of evolving power grids.

Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration process. The challenge lies in reducing the computational complexity while maintaining high accuracy for quick evaluations of multiple design alternatives. This research explores advanced methods, including surrogate models, reduced-order models (ROM), and multi-fidelity machine learning techniques, to achieve more efficient aircraft design evaluations. Specifically, the study investigates the application of Multi-fidelity Physics-Informed Neural Networks (MPINN) and autoencoders for manifold alignment, alongside the potential of Generative Adversarial Networks (GANs) for refining design geometries. Through a proof-of-concept task, the research demonstrates the ability to predict high-fidelity results from low-fidelity simulations, offering a path toward faster and more cost effective aircraft design iterations.

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.

In recent years, scientific machine learning (SciML) has emerged as a paradigm for modeling physical systems [1, 2, 3]. Typically using the theory of multilayer perceptrons (MLPs), SciML has shown great success in modeling a wide range of applications, however, data-informed training struggles when high-quality data is not available. Kolmogorov-Arnold networks (KANs) have recently been developed as an alternative to MLPs [4, 5]. KANs use the Kolmogorov-Arnold Theorem as inspiration and can offer advantages over MLPs in some cases, such as for discovering interpretable models. However, KANs have been shown to struggle to reach the accuracy of MLPs, particularly without modifications [6, 7, 8, 9]. In the short time since the publication of [4], many variations of KANs have been developed, including physics-informed KANs (PIKANs)[9], KAN-informed neural networks (KINNs)[10], temporal KANs [11], wavelet KANs [12], graph KANs [13, 14, 15], Chebyshev KANs (cKANs) [16], convolutional KANs [17], ReLU-KANs [18], Higher-order-ReLU-KANs (HRKANs) [19], fractional KANs [20], finite basis KANs [21], deep operator KANs [22], and others.

Damage prognosis is, arguably, one of the most difficult tasks of structural health monitoring (SHM). To address common problems of damage prognosis, a population-based SHM (PBSHM) approach is adopted in the current work. In this approach the prognosis problem is considered as an information-sharing problem where data from past structures are exploited to make more accurate inferences regarding currently-degrading structures. For a given population, there may exist restrictions on the resources available to conduct monitoring; thus, the current work studies the problem of allocating such resources within a population of degrading structures with a view to maximising the damage-prognosis accuracy. The challenges of the current framework are mainly associated with the inference of outliers on the level of damage evolution, given partial data from the damage-evolution phenomenon. The current approach considers an initial population of structures for which damage evolution is extensively observed. Subsequently, a second population of structures with evolving damage is considered for which two monitoring systems are available, a low-availability and high-fidelity (low-uncertainty) one, and a widely-available and low-fidelity (high-uncertainty) one. The task of the current work is to follow an active-learning approach to identify the structures to which the high-fidelity system should be assigned in order to enhance the predictive capabilities of the machine-learning model throughout the population.

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to define a multivariate Gaussian prior density for the coordinates of the true data points. In addition, few high-fidelity data points are used to construct a conjugate likelihood term. Thereafter, Bayes rule is applied to derive an explicit expression for the posterior density which is also multivariate Gaussian. The maximum \textit{a posteriori} (MAP) estimate of this density is selected to be the optimal multi-fidelity estimate. It is shown that the MAP estimate and the covariance of the posterior density can be determined through the solution of linear systems of equations. Thereafter, two methods, one based on spectral truncation and another based on a low-rank approximation, are developed to solve these equations efficiently. The multi-fidelity approach is tested on a variety of problems in solid and fluid mechanics with data that represents vectors of quantities of interest and discretized spatial fields in one and two dimensions. The results demonstrate that by utilizing a small fraction of high-fidelity data, the multi-fidelity approach can significantly improve the accuracy of a large collection of low-fidelity data points.