High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep neural networks (DNNs) as surrogate models capable of accelerating the simulations. However, existing approaches for training these DNN surrogates rely on extensive simulation data which are heuristically selected and generated with expensive computation -- a challenge under-explored in the literature. In this paper, we investigate the potential of incorporating active learning into DNN surrogate training. This allows intelligent and objective selection of training simulations, reducing the need to generate extensive simulation data as well as the dependency of the performance of DNN surrogates on pre-defined training simulations. In the problem context of constructing DNN surrogates for diffusion equations with sources, we examine the efficacy of diversity- and uncertainty-based strategies for selecting training simulations, considering two different DNN architecture. The results set the groundwork for developing the high-performance computing infrastructure for Smart Surrogates that supports on-the-fly generation of simulation data steered by active learning strategies to potentially improve the efficiency of scientific simulations.

Large Vision-Language Models (LVLMs) have shown significant potential in assisting medical diagnosis by leveraging extensive biomedical datasets. However, the advancement of medical image understanding and reasoning critically depends on building high-quality visual instruction data, which is costly and labor-intensive to obtain, particularly in the medical domain. To mitigate this data-starving issue, we introduce Self-Training Large Language and Vision Assistant for Medical (STLLaVA-Med). The proposed method is designed to train a policy model (an LVLM) capable of auto-generating medical visual instruction data to improve data efficiency, guided through Direct Preference Optimization (DPO). Specifically, a more powerful and larger LVLM (e.g., GPT-4o) is involved as a biomedical expert to oversee the DPO fine-tuning process on the auto-generated data, encouraging the policy model to align efficiently with human preferences. We validate the efficacy and data efficiency of STLLaVA-Med across three major medical Visual Question Answering (VQA) benchmarks, demonstrating competitive zero-shot performance with the utilization of only 9% of the medical data.

Personalized virtual heart models have demonstrated increasing potential for clinical use, although the estimation of their parameters given patient-specific data remain a challenge. Traditional physics-based modeling approaches are computationally costly and often neglect the inherent structural errors in these models due to model simplifications and assumptions. Modern deep learning approaches, on the other hand, rely heavily on data supervision and lacks interpretability. In this paper, we present a novel hybrid modeling framework to describe a personalized cardiac digital twin as a combination of a physics-based known expression augmented by neural network modeling of its unknown gap to reality. We then present a novel meta-learning framework to enable the separate identification of both the physics-based and neural components in the hybrid model. We demonstrate the feasibility and generality of this hybrid modeling framework with two examples of instantiations and their proof-of-concept in synthetic experiments.

Modern applications increasingly require unsupervised learning of latent dynamics from high-dimensional time-series. This presents a significant challenge of identifiability: many abstract latent representations may reconstruct observations, yet do they guarantee an adequate identification of the governing dynamics? This paper investigates this challenge from two angles: the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification. We combine these two strategies in a novel framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD) with: 1) a latent dynamic function that hybridize known mathematical expressions of prior physics with neural functions describing its unknown errors, and 2) a meta-learning formulation to learn to separately identify both components of the hybrid dynamics. Through extensive experiments on five physics and one biomedical systems, we provide strong evidence for the benefits of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to observed data.

The surgical environment imposes unique challenges to the intraoperative registration of organ shapes to their preoperatively-imaged geometry. Biomechanical model-based registration remains popular, while deep learning solutions remain limited due to the sparsity and variability of intraoperative measurements and the limited ground-truth deformation of an organ that can be obtained during the surgery. In this paper, we propose a novel \textit{hybrid} registration approach that leverage a linearized iterative boundary reconstruction (LIBR) method based on linear elastic biomechanics, and use deep neural networks to learn its residual to the ground-truth deformation (LIBR+). We further formulate a dual-branch spline-residual graph convolutional neural network (SR-GCN) to assimilate information from sparse and variable intraoperative measurements and effectively propagate it through the geometry of the 3D organ. Experiments on a large intraoperative liver registration dataset demonstrated the consistent improvements achieved by LIBR+ in comparison to existing rigid, biomechnical model-based non-rigid, and deep-learning based non-rigid approaches to intraoperative liver registration.

Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction solutions. In this work, we propose to embed the traditional mechanistic forward operator inside a neural function, and focus on modeling and correcting its unknown errors in an interpretable manner. This is achieved by a conditional generative model that transforms a given mechanistic operator with unknown errors, arising from a latent space of self-organizing clusters of potential sources of error generation. Once learned, the generative model can be used in place of a fixed forward operator in any traditional optimization-based reconstruction process where, together with the inverse solution, the error in prior mechanistic forward operator can be minimized and the potential source of error uncovered. We apply the presented method to the reconstruction of heart electrical potential from body surface potential. In controlled simulation experiments and in-vivo real data experiments, we demonstrate that the presented method allowed reduction of errors in the physics-based forward operator and thereby delivered inverse reconstruction of heart-surface potential with increased accuracy.

The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the behavior of the neural function on large unlabeled data. The smoothness of the neural function is a commonly used assumption exploited in SSL. A successful example is the adoption of mixup strategy in SSL that enforces the global smoothness of the neural function by encouraging it to behave linearly when interpolating between training examples. Despite its empirical success, however, the theoretical underpinning of how mixup regularizes the neural function has not been fully understood. In this paper, we offer a theoretically substantiated proposition that mixup improves the smoothness of the neural function by bounding the Lipschitz constant of the gradient function of the neural networks. We then propose that this can be strengthened by simultaneously constraining the Lipschitz constant of the neural function itself through adversarial Lipschitz regularization, encouraging the neural function to behave linearly while also constraining the slope of this linear function. On three benchmark data sets and one real-world biomedical data set, we demonstrate that this combined regularization results in improved generalization performance of SSL when learning from a small amount of labeled data. We further demonstrate the robustness of the presented method against single-step adversarial attacks. Our code is available at https://github.com/Prasanna1991/Mixup-LR.

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper, we present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph over the graphical embedding of the two geometry. We applied the presented network to reconstructing electrical activity on the heart surface from body-surface potential. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the presented network to generalize across geometrical changes underlying the data in comparison to its Euclidean alternatives.

Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty, if left unquantified, will lead to unknown variability in model outputs that hinder their reliable adoptions. Probabilistic estimation model parameters, however, remains an unresolved challenge because standard Markov Chain Monte Carlo sampling requires repeated model simulations that are computationally infeasible. A common solution is to replace the simulation model with a computationally-efficient surrogate for a faster sampling. However, by sampling from an approximation of the exact posterior probability density function (pdf) of the parameters, the efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling into Metropolis Hasting (MH) sampling of the exact posterior pdfs to improve its acceptance rate. It is done by first quickly constructing a Gaussian process (GP) surrogate of the exact posterior pdfs using deterministic optimization. This efficient surrogate is then used to modify commonly-used proposal distributions in MH sampling such that only proposals accepted by the surrogate will be tested by the exact posterior pdf for acceptance/rejection, reducing unnecessary model simulations at unlikely candidates. Synthetic and real-data experiments using the presented method show a significant gain in computational efficiency without compromising the accuracy. In addition, insights into the non-identifiability and heterogeneity of tissue properties can be gained from the obtained posterior distributions.

Computer-aided diagnosis via deep learning relies on large-scale annotated data sets, which can be costly when involving expert knowledge. Semi-supervised learning (SSL) mitigates this challenge by leveraging unlabeled data. One effective SSL approach is to regularize the local smoothness of neural functions via perturbations around single data points. In this work, we argue that regularizing the global smoothness of neural functions by filling the void in between data points can further improve SSL. We present a novel SSL approach that trains the neural network on linear mixing of labeled and unlabeled data, at both the input and latent space in order to regularize different portions of the network. We evaluated the presented model on two distinct medical image data sets for semi-supervised classification of thoracic disease and skin lesion, demonstrating its improved performance over SSL with local perturbations and SSL with global mixing but at the input space only. Our code is available at https://github.com/Prasanna1991/LatentMixing.