We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images.

This article presents a novel hybrid approach using statistics and machine learning to forecast the national demand of electricity. As investment and operation of future energy systems require long-term electricity demand forecasts with hourly resolution, our mathematical model fills a gap in energy forecasting. The proposed methodology was constructed using hourly data from Ukraine's electricity consumption ranging from 2013 to 2020. To this end, we analysed the underlying structure of the hourly, daily and yearly time series of electricity consumption. The long-term yearly trend is evaluated using macroeconomic regression analysis. The mid-term model integrates temperature and calendar regressors to describe the underlying structure, and combines ARIMA and LSTM ``black-box'' pattern-based approaches to describe the error term. The short-term model captures the hourly seasonality through calendar regressors and multiple ARMA models for the residual. Results show that the best forecasting model is composed by combining multiple regression models and a LSTM hybrid model for residual prediction. Our hybrid model is very effective at forecasting long-term electricity consumption on an hourly resolution. In two years of out-of-sample forecasts with 17520 timesteps, it is shown to be within 96.83 \% accuracy.

Graph neural networks (GNNs) have gained traction in high-energy physics (HEP) for their potential to improve accuracy and scalability. However, their resource-intensive nature and complex operations have motivated the development of symmetry-equivariant architectures. In this work, we introduce EuclidNet, a novel symmetry-equivariant GNN for charged particle tracking. EuclidNet leverages the graph representation of collision events and enforces rotational symmetry with respect to the detector's beamline axis, leading to a more efficient model. We benchmark EuclidNet against the state-of-the-art Interaction Network on the TrackML dataset, which simulates high-pileup conditions expected at the High-Luminosity Large Hadron Collider (HL-LHC). Our results show that EuclidNet achieves near-state-of-the-art performance at small model scales (< 1000 parameters), outperforming the non-equivariant benchmarks. This study paves the way for future investigations into more resource-efficient GNN models for particle tracking in HEP experiments.

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer models makes it computationally intensive to query them hundreds of times for optimization and one usually relies on a simplified model albeit at the cost of losing predictive accuracy and precision. Towards this, data-driven surrogate modeling methods have shown a lot of promise in emulating the behavior of the expensive computer models. However, a major bottleneck in such methods is the inability to deal with high input dimensionality and the need for relatively large datasets. With such problems, the input and output quantity of interest are tensors of high dimensionality. Commonly used surrogate modeling methods for such problems, suffer from requirements like high number of computational evaluations that precludes one from performing other numerical tasks like uncertainty quantification and statistical analysis. In this work, we propose an end-to-end approach that maps a high-dimensional image like input to an output of high dimensionality or its key statistics. Our approach uses two main framework that perform three steps: a) reduce the input and output from a high-dimensional space to a reduced or low-dimensional space, b) model the input-output relationship in the low-dimensional space, and c) enable the incorporation of domain-specific physical constraints as masks. In order to accomplish the task of reducing input dimensionality we leverage principal component analysis, that is coupled with two surrogate modeling methods namely: a) Bayesian hybrid modeling, and b) DeepHyper's deep neural networks. We demonstrate the applicability of the approach on a problem of a linear elastic stress field data.

Multivariate time series classification (MTSC) is an important data mining task, which can be effectively solved by popular deep learning technology. Unfortunately, the existing deep learning-based methods neglect the hidden dependencies in different dimensions and also rarely consider the unique dynamic features of time series, which lack sufficient feature extraction capability to obtain satisfactory classification accuracy. To address this problem, we propose a novel temporal dynamic graph neural network (TodyNet) that can extract hidden spatio-temporal dependencies without undefined graph structure. It enables information flow among isolated but implicit interdependent variables and captures the associations between different time slots by dynamic graph mechanism, which further improves the classification performance of the model. Meanwhile, the hierarchical representations of graphs cannot be learned due to the limitation of GNNs. Thus, we also design a temporal graph pooling layer to obtain a global graph-level representation for graph learning with learnable temporal parameters. The dynamic graph, graph information propagation, and temporal convolution are jointly learned in an end-to-end framework. The experiments on 26 UEA benchmark datasets illustrate that the proposed TodyNet outperforms existing deep learning-based methods in the MTSC tasks.

An active reconfigurable intelligent surface (RIS)-aided multi-user downlink communication system is investigated, where non-orthogonal multiple access (NOMA) is employed to improve spectral efficiency, and the active RIS is powered by energy harvesting (EH). The problem of joint control of the RIS's amplification matrix and phase shift matrix is formulated to maximize the communication success ratio with considering the quality of service (QoS) requirements of users, dynamic communication state, and dynamic available energy of RIS. To tackle this non-convex problem, a cascaded deep learning algorithm namely long short-term memory-deep deterministic policy gradient (LSTM-DDPG) is designed. First, an advanced LSTM based algorithm is developed to predict users' dynamic communication state. Then, based on the prediction results, a DDPG based algorithm is proposed to joint control the amplification matrix and phase shift matrix of the RIS. Finally, simulation results verify the accuracy of the prediction of the proposed LSTM algorithm, and demonstrate that the LSTM-DDPG algorithm has a significant advantage over other benchmark algorithms in terms of communication success ratio performance.

Data-driven intelligent computational design (DICD) is a research hotspot emerged under the context of fast-developing artificial intelligence. It emphasizes on utilizing deep learning algorithms to extract and represent the design features hidden in historical or fabricated design process data, and then learn the combination and mapping patterns of these design features for the purposes of design solution retrieval, generation, optimization, evaluation, etc. Due to its capability of automatically and efficiently generating design solutions and thus supporting human-in-the-loop intelligent and innovative design activities, DICD has drawn the attentions from both academic and industrial fields. However, as an emerging research subject, there are still many unexplored issues that limit the development and application of DICD, such as specific dataset building, engineering design related feature engineering, systematic methods and techniques for DICD implementation in the entire product design process, etc. In this regard, a systematic and operable road map for DICD implementation from full-process perspective is established, including a general workflow for DICD project planning, an overall framework for DICD project implementation, the computing mechanisms for DICD implementation, key enabling technologies for detailed DICD implementation, and three application scenarios of DICD. The road map reveals the common mechanisms and calculation principles of existing DICD researches, and thus it can provide systematic guidance for the possible DICD applications that have not been explored.

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the single sample path of the generic agent. We call this {\it Sandbox Learning}, as it can be used as a warm-start for any agent learning in a multi-agent non-cooperative setting. We adopt a two time-scale approach in which an online fixed-point recursion for the mean-field operates on a slower time-scale, in tandem with a control policy update on a faster time-scale for the generic agent. Given that the underlying Markov Decision Process (MDP) of the agent is communicating, we provide finite sample convergence guarantees in terms of convergence of the mean-field and control policy to the mean-field equilibrium. The sample complexity of the Sandbox learning algorithm is $\tilde{\mathcal{O}}(\epsilon^{-4})$ where $\epsilon$ is the MFE approximation error. This is similar to works which assume access to oracle. Finally, we empirically demonstrate the effectiveness of the sandbox learning algorithm in diverse scenarios, including those where the MDP does not necessarily have a single communicating class.

This paper proposes a real-time physically-based method for simulating vehicle deformation. Our system synthesizes vehicle deformation characteristics by considering a low-dimensional coupled vehicle body technique. We simulate the motion and crumbling behavior of vehicles smashing into rigid objects. We explain and demonstrate the combination of a reduced complexity non-linear finite element system that is scalable and computationally efficient. We use an explicit position-based integration scheme to improve simulation speeds, while remaining stable and preserving modeling accuracy. We show our approach using a variety of vehicle deformation test cases which were simulated in real-time.

As the potential of foundation models in visual tasks has garnered significant attention, pretraining these models before downstream tasks has become a crucial step. The three key factors in pretraining foundation models are the pretraining method, the size of the pretraining dataset, and the number of model parameters. Recently, research in the remote sensing field has focused primarily on the pretraining method and the size of the dataset, with limited emphasis on the number of model parameters. This paper addresses this gap by examining the effect of increasing the number of model parameters on the performance of foundation models in downstream tasks such as rotated object detection and semantic segmentation. We pretrained foundation models with varying numbers of parameters, including 86M, 605.26M, 1.3B, and 2.4B, to determine whether performance in downstream tasks improved with an increase in parameters. To the best of our knowledge, this is the first billion-scale foundation model in the remote sensing field. Furthermore, we propose an effective method for scaling up and fine-tuning a vision transformer in the remote sensing field. To evaluate general performance in downstream tasks, we employed the DOTA v2.0 and DIOR-R benchmark datasets for rotated object detection, and the Potsdam and LoveDA datasets for semantic segmentation. Experimental results demonstrated that, across all benchmark datasets and downstream tasks, the performance of the foundation models and data efficiency improved as the number of parameters increased. Moreover, our models achieve the state-of-the-art performance on several datasets including DIOR-R, Postdam, and LoveDA.