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We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a prox-simple function. The algorithm's special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal-dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal-dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function.

We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but also with consideration of its use within the conjugate gradient (CG) method. We propose three different strategies for selecting a scaling parameter, which aims to position the eigenvalues of the preconditioned matrix in a way that reduces the energy norm of the error, the quantity that CG monotonically decreases at each iteration. Our focus is on accelerating convergence especially in the early iterations, which is particularly important when CG is truncated due to computational cost constraints. Numerical experiments provide in data assimilation confirm that the scaled spectral preconditioner can significantly improve early CG convergence with negligible computational cost.

We develop a new computational framework to solve sequential Bayesian optimal experimental design (SBOED) problems constrained by large-scale partial differential equations with infinite-dimensional random parameters. We propose an adaptive terminal formulation of the optimality criteria for SBOED to achieve adaptive global optimality. We also establish an equivalent optimization formulation to achieve computational simplicity enabled by Laplace and low-rank approximations of the posterior. To accelerate the solution of the SBOED problem, we develop a derivative-informed latent attention neural operator (LANO), a new neural network surrogate model that leverages (1) derivative-informed dimension reduction for latent encoding, (2) an attention mechanism to capture the dynamics in the latent space, (3) an efficient training in the latent space augmented by projected Jacobian, which collectively leads to an efficient, accurate, and scalable surrogate in computing not only the parameter-to-observable (PtO) maps but also their Jacobians. We further develop the formulation for the computation of the MAP points, the eigenpairs, and the sampling from posterior by LANO in the reduced spaces and use these computations to solve the SBOED problem. We demonstrate the superior accuracy of LANO compared to two other neural architectures and the high accuracy of LANO compared to the finite element method (FEM) for the computation of MAP points and eigenvalues in solving the SBOED problem with application to the experimental design of the time to take MRI images in monitoring tumor growth. We show that the proposed computational framework achieves an amortized $180\times$ speedup.

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient training algorithms. In this work, we integrate concepts from pullback Riemannian geometry and generative models to propose a framework for data-driven Riemannian geometry that is scalable in both geometry and learning: score-based pullback Riemannian geometry. Focusing on unimodal distributions as a first step, we propose a score-based Riemannian structure with closed-form geodesics that pass through the data probability density. With this structure, we construct a Riemannian autoencoder (RAE) with error bounds for discovering the correct data manifold dimension. This framework can naturally be used with anisotropic normalizing flows by adopting isometry regularization during training. Through numerical experiments on various datasets, we demonstrate that our framework not only produces high-quality geodesics through the data support, but also reliably estimates the intrinsic dimension of the data manifold and provides a global chart of the manifold, even in high-dimensional ambient spaces.

The aim of this study is to establish a general transformation matrix between B-spline surfaces and ANCF surface elements. This study is a further study of the conversion between the ANCF and B-spline surfaces. In this paper, a general transformation matrix between the Bezier surfaces and ANCF surface element is established. This general transformation matrix essentially describes the linear relationship between ANCF and Bezier surfaces. Moreover, the general transformation matrix can help to improve the efficiency of the process to transfer the distorted configuration in the CAA back to the CAD, an urgent requirement in engineering practice. In addition, a special Bezier surface control polygon is given in this study. The Bezier surface described with this control polygon can be converted to an ANCF surface element with fewer d.o.f.. And the converted ANCF surface element with 36 d.o.f. was once addressed by Dufva and Shabana. So the special control polygon can be regarded as the geometric condition in conversion to an ANCF surface element with 36 d.o.f. Based on the fact that a B-spline surface can be seen as a set of Bezier surfaces connected together, the method to establish a general transformation matrix between the ANCF and lower-order B-spline surfaces is given. Specially, the general transformation is not in a recursive form, but in a simplified form.

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we provide exact characterizations of both the prediction error as well as the estimation error. Moreover, we show that these characterizations are universal: as long as the entries of the data matrix satisfy a set of independence and moment conditions, our guarantees continue to hold. Universality, in turn, enables the detailed study of several imputation-based strategies when the covariates are missing completely at random. We ground our study by comparing the performance of these strategies with the conjectured performance -- stemming from replica theory in statistical physics -- of the Bayes optimal procedure. Our analysis yields several insights including: (i) a distinction between single imputation and a simple variant of multiple imputation and (ii) that adding a simple ridge regularization term to single-imputed logistic regression can yield an estimator whose prediction error is nearly indistinguishable from the Bayes optimal prediction error. We supplement our findings with extensive numerical experiments.

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the BGK equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. The accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

Rodents employ a broad spectrum of ultrasonic vocalizations (USVs) for social communication. As these vocalizations offer valuable insights into affective states, social interactions, and developmental stages of animals, various deep learning approaches have aimed to automate both the quantitative (detection) and qualitative (classification) analysis of USVs. Here, we present the first systematic evaluation of different types of neural networks for USV classification. We assessed various feedforward networks, including a custom-built, fully-connected network and convolutional neural network, different residual neural networks (ResNets), an EfficientNet, and a Vision Transformer (ViT). Paired with a refined, entropy-based detection algorithm (achieving recall of 94.9% and precision of 99.3%), the best architecture (achieving 86.79% accuracy) was integrated into a fully automated pipeline capable of analyzing extensive USV datasets with high reliability. Additionally, users can specify an individual minimum accuracy threshold based on their research needs. In this semi-automated setup, the pipeline selectively classifies calls with high pseudo-probability, leaving the rest for manual inspection. Our study focuses exclusively on neonatal USVs. As part of an ongoing phenotyping study, our pipeline has proven to be a valuable tool for identifying key differences in USVs produced by mice with autism-like behaviors.

We develop a numerical method for simulation of incompressible viscous flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering method in LES, interpreted as spatial averaging, along with the integral representation theorem for parabolic equations, to achieve a closure scheme which may be used for calculating solutions of Navier-Stokes equations. This approach circumvents the challenge associated with handling the non-locally integrable 3-dimensional integral kernel in the random vortex method and facilitates the computation of numerical solutions for flow systems via Monte-Carlo method. Numerical simulations are carried out for both laminar and turbulent flows, demonstrating the validity and effectiveness of the method.

Computational fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing computational models for complex coupled systems can be challenging and time-consuming. In particular, ensuring the consistent integration of models from diverse physical domains requires meticulous attention. Even if the coupling of specialized simulation tools based on different formalisms were practically feasible, the growing demand to combine first-principles-based modeling with scientific machine learning necessitates an integrated high-level approach to model specification. Considering the example of electro-magneto hydrodynamics (on a fixed spatial domain and with linear polarization and magnetization), this article demonstrates how relatively complex models can be hierarchically composed from simpler parts by means of a formal language for multiphysics modeling. The Exergetic Port-Hamiltonian Systems (EPHS) modeling language features a simple graphical syntax for expressing the energy-based interconnection of subsystems. This reduces cognitive load and facilitates communication, especially in multidisciplinary environments. As the example demonstrates, existing models can be easily integrated as subsystems of new models. Specifically, the ideal fluid model is used as a subsystem of the Navier-Stokes-Fourier fluid model, which in turn is used as a subsystem of the electro-magneto hydrodynamics model. The compositional approach makes it nearly trivial to encapsulate, reuse, and swap out (parts of) models. Moreover, structural properties of EPHS models guarantee fundamental properties of thermodynamic systems, such as conservation of energy, non-negative entropy production, and Onsager reciprocal relations.