The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes (GPs) are candidate model choices for interpolation. However, due to their poor scalability, they usually rely on inducing points for inference, which restricts their expressivity. Moreover, commonly imposed assumptions such as stationarity prevents them from capturing complex patterns in the data. While deep GPs can overcome this issue, training and making inference with them are difficult, again requiring crude approximations via inducing points. In this work, we instead approach the problem through Bayesian deep learning, where spatiotemporal fields are represented by deep neural networks, whose layers share the inductive bias of stationary GPs on the plane/sphere via random feature expansions. This allows one to (1) capture high frequency patterns in the data, and (2) use mini-batched gradient descent for large scale training. The advent of earth observation systems have made it possible to monitor virtually all of earth's atmosphere and the ocean at unprecedented scales. This development has been pivotal to the understanding of anthropogenic impact on the environment, including global warming and rise in sea level. Hence, it is crucial that we are able to process the voluminous data effectively and extract maximal information from it to make better informed decisions in our path to achieving sustainable development goals. However, observations from satellite products are inherently sparse in space-time, requiring methods to effectively fill in the gap at unobserved locations (Le Traon et al., 1998). This typically relies on data assimilation techniques such as the ensemble Kalman filter (Evensen, 2003), which requires one to have access to a physical model that describes the evolution of the field.

Nowadays, electric robots play big role in many fields as they can replace humans and/or decrease the amount of load on humans. There are several types of robots that are present in the daily life, some of them are fully controlled by humans while others are programmed to be self-controlled. In addition there are self-control robots with partial human control. Robots can be classified into three major kinds: industry robots, autonomous robots and mobile robots. Industry robots are used in industries and factories to perform mankind tasks in the easier and faster way which will help in developing products. Typically industrial robots perform difficult and dangerous tasks, as they lift heavy objects, handle chemicals, paint and assembly work and so on. They are working all the time hour after hour, day by day with the same precision and they do not get tired which means that they do not make errors due to fatigue. Indeed, they are ideally suited to complete repetitive tasks.

We develop compositional learning algorithms for coupled dynamical systems. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parametrize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. The proposed compositional modeling framework and learning algorithms may be applied broadly to learn control-oriented models of dynamical systems in a variety of application areas, however, in this work, we focus on their application to the modeling of electrical networks. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated D.C. microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss, compression introduces a penalty on the number of iterations needed to reach a solution. In this work, we investigate how the iteration penalty depends on the interaction between compression and problem structure, in the context of non-convex stochastic optimization. We focus on linear compression schemes, where compression and decompression can be modeled as multiplication with a random matrix. We consider several distributions of matrices, among them random orthogonal matrices and matrices with random Gaussian entries. We find that in each case, the impact of compression on convergence can be quantified in terms of the norm of the Hessian of the objective, using a norm defined by the compression scheme. The analysis reveals that in certain cases, compression performance is related to low-rank structure or other spectral properties of the problem. In these cases, our bounds predict that the penalty introduced by compression is significantly reduced compared to worst-case bounds that only consider the compression level, ignoring problem data. We verify the theoretical findings on several optimization problems, including fine-tuning an image classification model.

Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at algorithmic level. This paper presents a kernel version of SCNs, termed KSCNs, aiming to enhance model's representation learning capability and performance stability. The random bases of a built SCN model can be used to span a reproducing kernel Hilbert space (RKHS), followed by our proposed algorithm for constructing KSCNs. It is shown that the data distribution in the reconstructive space is favorable for regression solving and the proposed KSCN learner models hold the universal approximation property. Three benchmark datasets including two industrial datasets are used in this study for performance evaluation. Experimental results with comparisons against existing solutions clearly demonstrate that the proposed KSCN remarkably outperforms the original SCNs and some typical kernel methods for resolving nonlinear regression problems in terms of the learning performance, the model's stability and robustness with respect to the kernel parameter settings.

Learning-based congestion controllers offer better adaptability compared to traditional heuristic algorithms. However, the inherent unreliability of learning techniques can cause learning-based controllers to behave poorly, creating a need for formal guarantees. While methods for formally verifying learned congestion controllers exist, these methods offer binary feedback that cannot optimize the controller toward better behavior. We improve this state-of-the-art via C3, a new learning framework for congestion control that integrates the concept of formal certification in the learning loop. C3 uses an abstract interpreter that can produce robustness and performance certificates to guide the training process, rewarding models that are robust and performant even on worst-case inputs. Our evaluation demonstrates that unlike state-of-the-art learned controllers, C3-trained controllers provide both adaptability and worst-case reliability across a range of network conditions.

Sound decision-making relies on accurate prediction for tangible outcomes ranging from military conflict to disease outbreaks. To improve crowdsourced forecasting accuracy, we developed SAGE, a hybrid forecasting system that combines human and machine generated forecasts. The system provides a platform where users can interact with machine models and thus anchor their judgments on an objective benchmark. The system also aggregates human and machine forecasts weighting both for propinquity and based on assessed skill while adjusting for overconfidence. We present results from the Hybrid Forecasting Competition (HFC) - larger than comparable forecasting tournaments - including 1085 users forecasting 398 real-world forecasting problems over eight months. Our main result is that the hybrid system generated more accurate forecasts compared to a human-only baseline which had no machine generated predictions. We found that skilled forecasters who had access to machine-generated forecasts outperformed those who only viewed historical data. We also demonstrated the inclusion of machine-generated forecasts in our aggregation algorithms improved performance, both in terms of accuracy and scalability. This suggests that hybrid forecasting systems, which potentially require fewer human resources, can be a viable approach for maintaining a competitive level of accuracy over a larger number of forecasting questions.

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant amount of overlap between adjacent scan locations, leading to large data volumes and prolonged acquisition times. To address this key limitation, this paper proposes a Bayesian inversion method for ptychography that performs effectively even with less overlap between neighboring scan locations. Furthermore, the proposed method can quantify the inherent uncertainty on the ptychographic object, which is created by the ill-posed nature of the ptychographic inverse problem. At a high level, the proposed method first utilizes a deep generative model to learn the prior distribution of the object and then generates samples from the posterior distribution of the object by using a Markov Chain Monte Carlo algorithm. Our results from simulated ptychography experiments show that the proposed framework can consistently outperform a widely used iterative reconstruction algorithm in cases of reduced overlap. Moreover, the proposed framework can provide uncertainty estimates that closely correlate with the true error, which is not available in practice. The project website is available here.

The rapid growth of the financial sector and the rising focus on Environmental, Social, and Governance (ESG) considerations highlight the need for advanced NLP tools. However, open-source LLMs proficient in both finance and ESG domains remain scarce. To address this gap, we introduce SusGen-30K, a category-balanced dataset comprising seven financial NLP tasks and ESG report generation, and propose TCFD-Bench, a benchmark for evaluating sustainability report generation. Leveraging this dataset, we developed SusGen-GPT, a suite of models achieving state-of-the-art performance across six adapted and two off-the-shelf tasks, trailing GPT-4 by only 2% despite using 7-8B parameters compared to GPT-4's 1,700B. Based on this, we propose the SusGen system, integrated with Retrieval-Augmented Generation (RAG), to assist in sustainability report generation. This work demonstrates the efficiency of our approach, advancing research in finance and ESG.