Stochastic Optimization for Nonconvex Problem With Inexact Hessian Matrix, Gradient, and Function.

Trust region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for nonconvex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the next search direction and the adjusted parameters. Although stochastic approximations help largely reduce the computational cost, it is challenging to theoretically guarantee the convergence rate. In this article, we explore a family of stochastic TR (STR) and stochastic ARC (SARC) methods that can simultaneously provide inexact computations of the Hessian matrix, gradient, and function values. Our algorithms require much fewer propagations overhead per iteration than TR and ARC. We prove that the iteration complexity to achieve ϵ -approximate second-order optimality is of the same order as the exact computations demonstrated in previous studies. In addition, the mild conditions on inexactness can be met by leveraging a random sampling technology in the finite-sum minimization problem. Numerical experiments with a nonconvex problem support these findings and demonstrate that, with the same or a similar number of iterations, our algorithms require less computational overhead per iteration than current second-order methods.

Trustworthy in silico cell labeling via ensemble-based image translation.

Artificial intelligence (AI) image translation has been a valuable tool for processing image data in biological and medical research. To apply such a tool in mission-critical applications, including drug screening, toxicity study, and clinical diagnostics, it is essential to ensure that the AI prediction is trustworthy. Here, we demonstrate that an ensemble learning method can quantify the uncertainty of AI image translation. We tested the uncertainty evaluation using experimentally acquired images of mesenchymal stromal cells. We find that the ensemble method reports a prediction standard deviation that correlates with the prediction error, estimating the prediction uncertainty. We show that this uncertainty is in agreement with the prediction error and Pearson correlation coefficient. We further show that the ensemble method can detect out-of-distribution input images by reporting increased uncertainty. Altogether, these results suggest that the ensemble-estimated uncertainty can be a useful indicator for identifying erroneous AI image translations.

Supracellular measurement of spatially varying mechanical heterogeneities in live monolayers.

The mechanical properties of tissues have profound impacts on a wide range of biological processes such as embryo development (1,2), wound healing (3-6), and disease progression (7). Specifically, the spatially varying moduli of cells largely influence the local tissue deformation and intercellular interaction. Despite the importance of characterizing such a heterogeneous mechanical property, it has remained difficult to measure the supracellular modulus field in live cell layers with a high-throughput and minimal perturbation. In this work, we developed a monolayer effective modulus measurement by integrating a custom cell stretcher, light microscopy, and AI-based inference. Our approach first quantifies the heterogeneous deformation of a slightly stretched cell layer and converts the measured strain fields into an effective modulus field using an AI inference. This method allowed us to directly visualize the effective modulus distribution of thousands of cells virtually instantly. We characterized the mean value, SD, and correlation length of the effective cell modulus for epithelial cells and fibroblasts, which are in agreement with previous results. We also observed a mild correlation between cell area and stiffness in jammed epithelia, suggesting the influence of cell modulus on packing. Overall, our reported experimental platform provides a valuable alternative cell mechanics measurement tool that can be integrated with microscopy-based characterizations.

Investigating heterogeneities of live mesenchymal stromal cells using AI-based label-free imaging.

Mesenchymal stromal cells (MSCs) are multipotent cells that have great potential for regenerative medicine, tissue repair, and immunotherapy. Unfortunately, the outcomes of MSC-based research and therapies can be highly inconsistent and difficult to reproduce, largely due to the inherently significant heterogeneity in MSCs, which has not been well investigated. To quantify cell heterogeneity, a standard approach is to measure marker expression on the protein level via immunochemistry assays. Performing such measurements non-invasively and at scale has remained challenging as conventional methods such as flow cytometry and immunofluorescence microscopy typically require cell fixation and laborious sample preparation. Here, we developed an artificial intelligence (AI)-based method that converts transmitted light microscopy images of MSCs into quantitative measurements of protein expression levels. By training a U-Net+ conditional generative adversarial network (cGAN) model that accurately (mean [Formula: see text] = 0.77) predicts expression of 8 MSC-specific markers, we showed that expression of surface markers provides a heterogeneity characterization that is complementary to conventional cell-level morphological analyses. Using this label-free imaging method, we also observed a multi-marker temporal-spatial fluctuation of protein distributions in live MSCs. These demonstrations suggest that our AI-based microscopy can be utilized to perform quantitative, non-invasive, single-cell, and multi-marker characterizations of heterogeneous live MSC culture. Our method provides a foundational step toward the instant integrative assessment of MSC properties, which is critical for high-throughput screening and quality control in cellular therapies.