Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the theory of kinematic growth, where the deformation gradient is multiplicatively decomposed into an elastic part and a part related to growth and remodeling. Recently, the concept of homeostatic surfaces was introduced to define the state of homeostasis and the evolution equations for inelastic deformations. However, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. In this work, we extend our inelastic Constitutive Artificial Neural Networks (iCANNs) by incorporating kinematic growth and homeostatic surfaces to discover the scalar model equations, namely the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.

Quality sleep is very important for a healthy life. Nowadays, many people around the world are not getting enough sleep which is having negative impacts on their lifestyles. Studies are being conducted for sleep monitoring and have now become an important tool for understanding sleep behavior. The gold standard method for sleep analysis is polysomnography (PSG) conducted in a clinical environment but this method is both expensive and complex for long-term use. With the advancements in the field of sensors and the introduction of off-the-shelf technologies, unobtrusive solutions are becoming common as alternatives for in-home sleep monitoring. Various solutions have been proposed using both wearable and non-wearable methods which are cheap and easy to use for in-home sleep monitoring. In this paper, we present a comprehensive survey of the latest research works (2015 and after) conducted in various categories of sleep monitoring including sleep stage classification, sleep posture recognition, sleep disorders detection, and vital signs monitoring. We review the latest works done using the non-invasive approach and cover both wearable and non-wearable methods. We discuss the design approaches and key attributes of the work presented and provide an extensive analysis based on 10 key factors, to give a comprehensive overview of the recent developments and trends in all four categories of sleep monitoring. We also present some publicly available datasets for different categories of sleep monitoring. In the end, we discuss several open issues and provide future research directions in the area of sleep monitoring.

Aquatic mammals, such as pinnipeds, utilize their whiskers to detect and discriminate objects and analyze water movements, inspiring the development of robotic whiskers for sensing contacts, surfaces, and water flows. We present the design and application of underwater whisker sensors based on Fiber Bragg Grating (FBG) technology. These passive whiskers are mounted along the robot$'$s exterior to sense its surroundings through light, non-intrusive contacts. For contact tracking, we employ a sim-to-real learning framework, which involves extensive data collection in simulation followed by a sim-to-real calibration process to transfer the model trained in simulation to the real world. Experiments with whiskers immersed in water indicate that our approach can track contact points with an accuracy of $<2$ mm, without requiring precise robot proprioception. We demonstrate that the approach also generalizes to unseen objects.

In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good starting model to avoid producing non-physical solutions. Moreover, conventional optimization methods fail to quantify the uncertainty associated with the recovered solution, which is critical for decision-making processes. Bayesian inference offers an alternative approach as it directly or indirectly evaluates the posterior probability density function. For example, Markov Chain Monte Carlo (MCMC) methods generate multiple sample chains to characterize the solution's uncertainty. Despite their ability to theoretically handle any form of distribution, MCMC methods require many sampling steps; this limits their usage in high-dimensional problems with computationally intensive forward modeling, as is the FWI case. Variational Inference (VI), on the other hand, provides an approximate solution to the posterior distribution in the form of a parametric or non-parametric proposal distribution. Among the various algorithms used in VI, Stein Variational Gradient Descent (SVGD) is recognized for its ability to iteratively refine a set of samples to approximate the target distribution. However, mode and variance-collapse issues affect SVGD in high-dimensional inverse problems. This study aims to improve the performance of SVGD within the context of FWI by utilizing, for the first time, an annealed variant of SVGD and combining it with a multi-scale strategy. Additionally, we demonstrate that Principal Component Analysis (PCA) can be used to evaluate the performance of the optimization process. Clustering techniques are also employed to provide more rigorous and meaningful statistical analysis of the particles in the presence of multi-modal distributions.

The Proper Orthogonal Decomposition (POD) computes the optimal basis modes that span a low-dimensional subspace where the Reduced-Order Models (ROMs) reside. Because a governing equation is often parameterized by a set of parameters, challenges immediately arise when one would like to investigate how systems behave differently over the parameter space (in design, control, uncertainty quantification and real-time operations). In this case, the POD basis needs to be updated so as to adapt ROM that accurately captures the variation of a system's behavior over its parameter space. This paper proposes a Projected Gaussian Process (pGP) and formulate the problem of adapting POD basis as a supervised statistical learning problem, for which the goal is to learn a mapping from the parameter space to the Grassmann Manifold that contains the optimal vector subspaces. A mapping is firstly found between the Euclidean space and the horizontal space of an orthogonal matrix that spans a reference subspace in the Grassmann Manifold. Then, a second mapping from the horizontal space to the Grassmann Manifold is established through the Exponential/Logarithm maps between the manifold and its tangent space. Finally, given a new parameter, the conditional distribution of a vector can be found in the Euclidean space using the Gaussian Process (GP) regression, and such a distribution is projected to the Grassmann Manifold that yields the optimal subspace for the new parameter. The proposed statistical learning approach allows us to optimally estimate model parameters given data (i.e., the prediction/interpolation becomes problem-specific), and quantify the uncertainty associated with the prediction. Numerical examples are presented to demonstrate the advantages of the proposed pGP for adapting POD basis against parameter changes.

The increasing severity of climate change necessitates an urgent transition to renewable energy sources, making the large-scale adoption of wind energy crucial for mitigating environmental impact. However, the inherent uncertainty of wind power poses challenges for grid stability, underscoring the need for accurate wind energy prediction models to enable effective power system planning and operation. While many existing studies on wind power prediction focus on short-term forecasting, they often overlook the importance of long-term predictions. Long-term wind power forecasting is essential for effective power grid dispatch and market transactions, as it requires careful consideration of weather features such as wind speed and direction, which directly influence power output. Consequently, methods designed for short-term predictions may lead to inaccurate results and high computational costs in long-term settings. To adress these limitations, we propose a novel approach called Hybrid Frequency Feature Enhancement Inverted Transformer (Hiformer). Hiformer introduces a unique structure that integrates signal decomposition technology with weather feature extraction technique to enhance the modeling of correlations between meteorological conditions and wind power generation. Additionally, Hiformer employs an encoder-only architecture, which reduces the computational complexity associated with long-term wind power forecasting. Compared to the state-of-the-art methods, Hiformer: (i) can improve the prediction accuracy by up to 52.5\%; and (ii) can reduce computational time by up to 68.5\%.

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks a comprehensive understanding. This is particularly true for deep time series forecasting methods, where analysis and understanding work is relatively limited. Time series data, unlike image and text information, can be more challenging to interpret and analyze. To address this, we approach the problem from a manifold learning perspective, assuming that the latent representations of time series forecasting models lie next to a low-dimensional manifold. In our study, we focus on analyzing the geometric features of these latent data manifolds, including intrinsic dimension and principal curvatures. Our findings reveal that deep transformer models exhibit similar geometric behavior across layers, and these geometric features are correlated with model performance. Additionally, we observe that untrained models initially have different structures, but they rapidly converge during training. By leveraging our geometric analysis and differentiable tools, we can potentially design new and improved deep forecasting neural networks. This approach complements existing analysis studies and contributes to a better understanding of transformer models in the context of time series forecasting. Code is released at https://github.com/azencot-group/GATLM.

The interaction of waves with structural barriers such as dams breaking plays a critical role in flood defense and tsunami disasters. In this work, we explore the dynamic changes in wave surfaces impacting various structural shapes, e.g., circle, triangle, and square, by using deep learning techniques. We introduce the DamFormer, a novel transformer-based model designed to learn and simulate these complex interactions. The model was trained and tested on simulated data representing the three structural forms.

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

To validate the second-by-second dynamics of turbines in field experiments, it is necessary to accurately reconstruct the winds going into the turbine. Current time-resolved inflow reconstruction techniques estimate wind behavior in unobserved regions using relatively simple spectral-based models of the atmosphere. Here, we develop a technique for time-resolved inflow reconstruction that is rooted in a large-eddy simulation model of the atmosphere. Our "large-eddy reconstruction" technique blends observations and atmospheric model information through a diffusion model machine learning algorithm, allowing us to generate probabilistic ensembles of reconstructions for a single 10-min observational period. Our generated inflows can be used directly by aeroelastic codes or as inflow boundary conditions in a large-eddy simulation. We verify the second-by-second reconstruction capability of our technique in three synthetic field campaigns, finding positive Pearson correlation coefficient values (0.20>r>0.85) between ground-truth and reconstructed streamwise velocity, as well as smaller positive correlation coefficient values for unobserved fields (spanwise velocity, vertical velocity, and temperature). We validate our technique in three real-world case studies by driving large-eddy simulations with reconstructed inflows and comparing to independent inflow measurements. The reconstructions are visually similar to measurements, follow desired power spectra properties, and track second-by-second behavior (0.25 > r > 0.75).