To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon giving the training data, whose leaf nodes represent different regions where region-specific neural networks are trained to predict both the mean and the variance for quantifying uncertainty. The proposed Uncertainty-Splitting Neural Regression Tree (USNRT) employs novel splitting criteria. At each node, a neural network is trained on the full data first, and a statistical test for the residuals is conducted to find the best split, corresponding to the two sub-regions with the most significant uncertainty heterogeneity between them. USNRT is computationally friendly because very few leaf nodes are sufficient and pruning is unnecessary. Furthermore, an ensemble version can be easily constructed to estimate the total uncertainty including the aleatory and epistemic. On extensive UCI datasets, USNRT or its ensemble shows superior performance compared to some recent popular methods for quantifying uncertainty with variances. Through comprehensive visualization and analysis, we uncover how USNRT works and show its merits, revealing that uncertainty heterogeneity does exist in many datasets and can be learned by USNRT.

Unsupervised source separation involves unraveling an unknown set of source signals recorded through a mixing operator, with limited prior knowledge about the sources, and only access to a dataset of signal mixtures. This problem is inherently ill-posed and is further challenged by the variety of time-scales exhibited by sources in time series data from planetary space missions. As such, a systematic multiscale unsupervised approach is needed to identify and separate sources at different time-scales. Existing methods typically rely on a preselected window size that determines their operating time-scale, limiting their capacity to handle multi-scale sources. To address this issue, instead of directly operating in the time domain, we propose an unsupervised multi-scale clustering and source separation framework by leveraging wavelet scattering covariances that provide a low-dimensional representation of stochastic processes, capable of effectively distinguishing between different non-Gaussian stochastic processes. Nested within this representation space, we develop a factorial Gaussian-mixture variational autoencoder that is trained to (1) probabilistically cluster sources at different time-scales and (2) independently sample scattering covariance representations associated with each cluster. As the final stage, using samples from each cluster as prior information, we formulate source separation as an optimization problem in the wavelet scattering covariance representation space, resulting in separated sources in the time domain. When applied to seismic data recorded during the NASA InSight mission on Mars, containing sources varying greatly in time-scale, our multi-scale nested approach proves to be a powerful tool for discriminating between such different sources, e.g., minute-long transient one-sided pulses (known as "glitches") and structured ambient noises resulting from atmospheric activities that typically last for tens of minutes. These results provide an opportunity to conduct further investigations into the isolated sources related to atmospheric-surface interactions, thermal relaxations, and other complex phenomena.

Proximity sensing detects an object's presence without contact. However, research has rarely explored proximity sensing in granular materials (GM) due to GM's lack of visual and complex properties. In this paper, we propose a granular-material-embedded autonomous proximity sensing system (GRAINS) based on three granular phenomena (fluidization, jamming, and failure wedge zone). GRAINS can automatically sense buried objects beneath GM in real-time manner (at least ~20 hertz) and perceive them 0.5 ~ 7 centimeters ahead in different granules without the use of vision or touch. We introduce a new spiral trajectory for the probe raking in GM, combining linear and circular motions, inspired by a common granular fluidization technique. Based on the observation of force-raising when granular jamming occurs in the failure wedge zone in front of the probe during its raking, we employ Gaussian process regression to constantly learn and predict the force patterns and detect the force anomaly resulting from granular jamming to identify the proximity sensing of buried objects. Finally, we apply GRAINS to a Bayesian-optimization-algorithm-guided exploration strategy to successfully localize underground objects and outline their distribution using proximity sensing without contact or digging. This work offers a simple yet reliable method with potential for safe operation in building habitation infrastructure on an alien planet without human intervention.

In this paper, we propose an enhanced approach for Rapid Exploration and eXploitation for AI Agents called REX. Existing AutoGPT-style techniques have inherent limitations, such as a heavy reliance on precise descriptions for decision-making, and the lack of a systematic approach to leverage try-and-fail procedures akin to traditional Reinforcement Learning (RL). REX introduces an additional layer of rewards and integrates concepts similar to Upper Confidence Bound (UCB) scores, leading to more robust and efficient AI agent performance. This approach has the advantage of enabling the utilization of offline behaviors from logs and allowing seamless integration with existing foundation models while it does not require any model fine-tuning. Through comparative analysis with existing methods such as Chain-of-Thoughts(CoT) and Reasoning viA Planning(RAP), REX-based methods demonstrate comparable performance and, in certain cases, even surpass the results achieved by these existing techniques. Notably, REX-based methods exhibit remarkable reductions in execution time, enhancing their practical applicability across a diverse set of scenarios.

Networked control systems are closed-loop feedback control systems containing system components that may be distributed geographically in different locations and interconnected via a communication network such as the Internet. The quality of network communication is a crucial factor that significantly affects the performance of remote control. This is due to the fact that network uncertainties can occur in the transmission of packets in the forward and backward channels of the system. The two most significant among these uncertainties are network time delay and packet loss. To overcome these challenges, the networked predictive control system has been proposed to provide improved performance and robustness using predictive controllers and compensation strategies. In particular, the model predictive control method is well-suited as an advanced approach compared to conventional methods. In this paper, a networked model predictive control system consisting of a model predictive control method and compensation strategies is implemented to control and stabilize a robot arm as a physical system. In particular, this work aims to analyze the performance of the system under the influence of network time delay and packet loss. Using appropriate performance and robustness metrics, an in-depth investigation of the impacts of these network uncertainties is performed. Furthermore, the forward and backward channels of the network are examined in detail in this study.

The molten sand, a mixture of calcia, magnesia, alumina, and silicate, known as CMAS, is characterized by its high viscosity, density, and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics (mDPD) simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a coarse parametric ordinary differential equation (ODE) that captures the spreading radius behavior of the CMAS droplets. The ODE parameters are then identified based on the Physics-Informed Neural Network (PINN) framework. Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modeling and state-of-the-art machine learning techniques.

The use of machine learning in algorithmic trading systems is increasingly common. In a typical set-up, supervised learning is used to predict the future prices of assets, and those predictions drive a simple trading and execution strategy. This is quite effective when the predictions have sufficient signal, markets are liquid, and transaction costs are low. However, those conditions often do not hold in thinly traded financial markets and markets for differentiated assets such as real estate or vehicles. In these markets, the trading strategy must consider the long-term effects of taking positions that are relatively more difficult to change. In this work, we propose a Reinforcement Learning (RL) algorithm that trades based on signals from a learned predictive model and addresses these challenges. We test our algorithm on 20+ years of equity data from Bursa Malaysia.

Efficient and sustainable power generation is a crucial concern in the energy sector. In particular, thermal power plants grapple with accurately predicting steam mass flow, which is crucial for operational efficiency and cost reduction. In this study, we use a parallel hybrid neural network architecture that combines a parametrized quantum circuit and a conventional feed-forward neural network specifically designed for time-series prediction in industrial settings to enhance predictions of steam mass flow 15 minutes into the future. Our results show that the parallel hybrid model outperforms standalone classical and quantum models, achieving more than 5.7 and 4.9 times lower mean squared error (MSE) loss on the test set after training compared to pure classical and pure quantum networks, respectively. Furthermore, the hybrid model demonstrates smaller relative errors between the ground truth and the model predictions on the test set, up to 2 times better than the pure classical model. These findings contribute to the broader scientific understanding of how integrating quantum and classical machine learning techniques can be applied to real-world challenges faced by the energy sector, ultimately leading to optimized power plant operations.

We train graph neural networks to perform field-level likelihood-free inference using galaxy catalogs from state-of-the-art hydrodynamic simulations of the CAMELS project. Our models are rotational, translational, and permutation invariant and do not impose any cut on scale. From galaxy catalogs that only contain $3$D positions and radial velocities of $\sim 1, 000$ galaxies in tiny $(25~h^{-1}{\rm Mpc})^3$ volumes our models can infer the value of $\Omega_{\rm m}$ with approximately $12$ % precision. More importantly, by testing the models on galaxy catalogs from thousands of hydrodynamic simulations, each having a different efficiency of supernova and AGN feedback, run with five different codes and subgrid models - IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE -, we find that our models are robust to changes in astrophysics, subgrid physics, and subhalo/galaxy finder. Furthermore, we test our models on $1,024$ simulations that cover a vast region in parameter space - variations in $5$ cosmological and $23$ astrophysical parameters - finding that the model extrapolates really well. Our results indicate that the key to building a robust model is the use of both galaxy positions and velocities, suggesting that the network have likely learned an underlying physical relation that does not depend on galaxy formation and is valid on scales larger than $\sim10~h^{-1}{\rm kpc}$.

In the context of digital twins, structural health monitoring (SHM) constitutes the backbone of condition-based maintenance, facilitating the interconnection between virtual and physical assets. Guided wave propagation (GWP) is commonly employed for the inspection of structures in SHM. However, GWP is sensitive to variations in the material properties of the structure, leading to false alarms. In this direction, uncertainty quantification (UQ) is regularly applied to improve the reliability of predictions. Computational mechanics is a useful tool for the simulation of GWP, and is often applied for UQ. Even so, the application of UQ methods requires numerous simulations, while large-scale, transient numerical GWP solutions increase the computational cost. Reduced order models (ROMs) are commonly employed to provide numerical results in a limited amount of time. In this paper, we propose a machine learning (ML)-based ROM, mentioned as BO-ML-ROM, to decrease the computational time related to the simulation of the GWP. The ROM is integrated with a Bayesian optimization (BO) framework, to adaptively sample the parameters for the ROM training. The finite element method is used for the simulation of the high-fidelity models. The formulated ROM is used for forward UQ of the GWP in an aluminum plate with varying material properties. To determine the influence of each parameter perturbation, a global, variance-based sensitivity analysis is implemented based on Sobol' indices. It is shown that Bayesian optimization outperforms one-shot sampling methods, both in terms of accuracy and speed-up. The predicted results reveal the efficiency of BO-ML-ROM for GWP and demonstrate its value for UQ.