The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are trained to satisfy partial differential equations (PDEs). While this method shows promise, the standard version has been shown to struggle in accurately predicting the dynamic behavior of time-dependent problems. To address this challenge, methods have been proposed that decompose the time domain into multiple segments, employing a distinct neural network in each segment and directly incorporating continuity between them in the loss function of the minimization problem. In this work we introduce a method to exactly enforce continuity between successive time segments via a solution ansatz. This hard constrained sequential PINN (HCS-PINN) method is simple to implement and eliminates the need for any loss terms associated with temporal continuity. The method is tested for a number of benchmark problems involving both linear and non-linear PDEs. Examples include various first order time dependent problems in which traditional PINNs struggle, namely advection, Allen-Cahn, and Korteweg-de Vries equations. Furthermore, second and third order time-dependent problems are demonstrated via wave and Jerky dynamics examples, respectively. Notably, the Jerky dynamics problem is chaotic, making the problem especially sensitive to temporal accuracy. The numerical experiments conducted with the proposed method demonstrated superior convergence and accuracy over both traditional PINNs and the soft-constrained counterparts.

The optimization of a black-box simulator over control parameters $\mathbf{x}$ arises in a myriad of scientific applications. In such applications, the simulator often takes the form $f(\mathbf{x},\boldsymbol{\theta})$, where $\boldsymbol{\theta}$ are parameters that are uncertain in practice. Robust optimization aims to optimize the objective $\mathbb{E}[f(\mathbf{x},\boldsymbol{\Theta})]$, where $\boldsymbol{\Theta} \sim \mathcal{P}$ is a random variable that models uncertainty on $\boldsymbol{\theta}$. For this, existing black-box methods typically employ a two-stage approach for selecting the next point $(\mathbf{x},\boldsymbol{\theta})$, where $\mathbf{x}$ and $\boldsymbol{\theta}$ are optimized separately via different acquisition functions. As such, these approaches do not employ a joint acquisition over $(\mathbf{x},\boldsymbol{\theta})$, and thus may fail to fully exploit control-to-noise interactions for effective robust optimization. To address this, we propose a new Bayesian optimization method called Targeted Variance Reduction (TVR). The TVR leverages a novel joint acquisition function over $(\mathbf{x},\boldsymbol{\theta})$, which targets variance reduction on the objective within the desired region of improvement. Under a Gaussian process surrogate on $f$, the TVR acquisition can be evaluated in closed form, and reveals an insightful exploration-exploitation-precision trade-off for robust black-box optimization. The TVR can further accommodate a broad class of non-Gaussian distributions on $\mathcal{P}$ via a careful integration of normalizing flows. We demonstrate the improved performance of TVR over the state-of-the-art in a suite of numerical experiments and an application to the robust design of automobile brake discs under operational uncertainty.

Feature selection prepares the AI-readiness of data by eliminating redundant features. Prior research falls into two primary categories: i) Supervised Feature Selection, which identifies the optimal feature subset based on their relevance to the target variable; ii) Unsupervised Feature Selection, which reduces the feature space dimensionality by capturing the essential information within the feature set instead of using target variable. However, SFS approaches suffer from time-consuming processes and limited generalizability due to the dependence on the target variable and downstream ML tasks. UFS methods are constrained by the deducted feature space is latent and untraceable. To address these challenges, we introduce an innovative framework for feature selection, which is guided by knockoff features and optimized through reinforcement learning, to identify the optimal and effective feature subset. In detail, our method involves generating "knockoff" features that replicate the distribution and characteristics of the original features but are independent of the target variable. Each feature is then assigned a pseudo label based on its correlation with all the knockoff features, serving as a novel metric for feature evaluation. Our approach utilizes these pseudo labels to guide the feature selection process in 3 novel ways, optimized by a single reinforced agent: 1). A deep Q-network, pre-trained with the original features and their corresponding pseudo labels, is employed to improve the efficacy of the exploration process in feature selection. 2). We introduce unsupervised rewards to evaluate the feature subset quality based on the pseudo labels and the feature space reconstruction loss to reduce dependencies on the target variable. 3). A new {\epsilon}-greedy strategy is used, incorporating insights from the pseudo labels to make the feature selection process more effective.

Machine learning techniques have been successfully used in probabilistic wind power forecasting. However, the issue of missing values within datasets due to sensor failure, for instance, has been overlooked for a long time. Although it is natural to consider addressing this issue by imputing missing values before model estimation and forecasting, we suggest treating missing values and forecasting targets indifferently and predicting all unknown values simultaneously based on observations. In this paper, we offer an efficient probabilistic forecasting approach by estimating the joint distribution of features and targets based on a generative model. It is free of preprocessing, and thus avoids introducing potential errors. Compared with the traditional "impute, then predict" pipeline, the proposed approach achieves better performance in terms of continuous ranked probability score.

The challenge of spatial resource allocation is pervasive across various domains such as transportation, industry, and daily life. As the scale of real-world issues continues to expand and demands for real-time solutions increase, traditional algorithms face significant computational pressures, struggling to achieve optimal efficiency and real-time capabilities. In recent years, with the escalating computational power of computers, the remarkable achievements of reinforcement learning in domains like Go and robotics have demonstrated its robust learning and sequential decision-making capabilities. Given these advancements, there has been a surge in novel methods employing reinforcement learning to tackle spatial resource allocation problems. These methods exhibit advantages such as rapid solution convergence and strong model generalization abilities, offering a new perspective on resolving spatial resource allocation problems. Therefore, this paper aims to summarize and review recent theoretical methods and applied research utilizing reinforcement learning to address spatial resource allocation problems. It provides a summary and comprehensive overview of its fundamental principles, related methodologies, and applied research. Additionally, it highlights several unresolved issues that urgently require attention in this direction for the future.

In light of this goal, adaptNMT has been developed This application is built upon the widelyadopted to provide users with a form of Explainable OpenNMT ecosystem, and is particularly Neural Machine Translation (XNMT). The useful for new entrants to the typical NMT process comprises several independent field, as it simplifies the setup of the development stages, including setting up the environment, environment and creation of train, preparing the dataset, training subword models, validation, and test splits. The application parameterizing and training the main models, evaluating offers a graphing feature that illustrates the and deploying them. By adopting a modular progress of model training, and employs approach, this framework has established an effective SentencePiece for creating subword segmentation NMT model development process that caters models. Furthermore, the application to both technical and non-technical practitioners in provides an intuitive user interface the field. To address the environmental impact of that facilitates hyperparameter customization.

Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called $\texttt{MultiDimSPCI}$ that builds prediction regions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate finite-sample high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that $\texttt{MultiDimSPCI}$ maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low computational requirements, but also their weakness: they struggle to represent fundamental dynamical balances, and they are far from being suitable for data assimilation experiments. Hybrid modelling emerges as a promising approach to address these limitations. Hybrid models integrate a physics-based core component with a statistical component, typically a neural network, to enhance prediction capabilities. In this article, we propose to develop a model error correction for the operational Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts using a neural network. The neural network is initially pre-trained offline using a large dataset of operational analyses and analysis increments. Subsequently, the trained network is integrated into the IFS within the Object-Oriented Prediction System (OOPS) so as to be used in data assimilation and forecast experiments. It is then further trained online using a recently developed variant of weak-constraint 4D-Var. The results show that the pre-trained neural network already provides a reliable model error correction, which translates into reduced forecast errors in many conditions and that the online training further improves the accuracy of the hybrid model in many conditions.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

Legged robots have demonstrated high efficiency and effectiveness in unstructured and dynamic environments. However, it is still challenging for legged robots to achieve rapid and efficient locomotion on deformable, yielding substrates, such as granular terrains. We present an enhanced resistive force model for bipedal walkers on soft granular terrains by introducing effective intrusion depth correction. The enhanced force model captures fundamental kinetic results considering the robot foot shape, walking gait speed variation, and energy expense. The model is validated by extensive foot intrusion experiments with a bipedal robot. The results confirm the model accuracy on the given type of granular terrains. The model can be further integrated with the motion control of bipedal robotic walkers.