A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. Motivated by the underlying mathematical structure, NIO is based on a suitable composition of DeepONets and FNOs to approximate mappings from operators to functions. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.

We study pure exploration with infinitely many bandit arms generated i.i.d. from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$ of being among the top $\eta$-fraction of arms; this is a natural adaptation of the classical PAC guarantee for infinite action sets. We consider both the fixed confidence and fixed budget settings, aiming respectively for minimal expected and fixed sample complexity. For fixed confidence, we give an algorithm with expected sample complexity $O\left(\frac{\log (1/\eta)\log (1/\delta)}{\eta\varepsilon^2}\right)$. This is optimal except for the $\log (1/\eta)$ factor, and the $\delta$-dependence closes a quadratic gap in the literature. For fixed budget, we show the asymptotically optimal sample complexity as $\delta\to 0$ is $c^{-1}\log(1/\delta)\big(\log\log(1/\delta)\big)^2$ to leading order. Equivalently, the optimal failure probability given exactly $N$ samples decays as $\exp\big(-cN/\log^2 N\big)$, up to a factor $1\pm o_N(1)$ inside the exponent. The constant $c$ depends explicitly on the problem parameters (including the unknown arm distribution) through a certain Fisher information distance. Even the strictly super-linear dependence on $\log(1/\delta)$ was not known and resolves a question of Grossman and Moshkovitz (FOCS 2016, SIAM Journal on Computing 2020).

Over a couple of decades, space junk has increased rapidly, which has caused significant threats to the LEO operation satellites. An Active Debris Removal $(ADR)$ concept continuously evolves for space junk removal. One of the ADR methods is Space Robotics, whose function is to chase, capture and de-orbit the space junk. This paper presents the development of an on-ground space robotics facility in the TCS Research for on-orbit servicing $(OOS)$ like refueling and debris capture experiments. A Hardware in Loop Simulation (HILS) system will be used for integrated system development, testing, and demonstration of on-orbit docking mechanisms. The HiLS test facility of TCS Research Lab will use two URs in which one UR is attached to the RG2 gripper, and the other is attached to a force-torque sensor and with a scaled mock-up model. The first UR5 will be mounted on a 7-axis linear rail and contain the docking probe. First, UR5 with a suitable gripper has to interface its control boxes. The grasping algorithm was run through the ROS interface line to demonstrate and validate the on-orbit operations. The manipulator will be mounted with LIDAR and a camera to visualize the mock-up model, find the target model's pose and rotational velocity estimation, and a gripper that will move relative to the target model. The other manipulator has the UR10 control, providing rotational and random motion to the mockup, enabling a dynamic simulator fed by force-torque data. The dynamic simulator is fed up with the orbit propagator, which will provide the orbiting environment to the target model. For the simulation of the docking and grasping of the target model, a linear rail of a 6m setup is still in the procurement process. Once reaching proximity, the grasping algorithm will be launched to capture the target model after reading the random motion of the mock-up model.

Contrastive learning methods have been applied to a range of domains and modalities by training models to identify similar "views" of data points. However, specialized scientific modalities pose a challenge for this paradigm, as identifying good views for each scientific instrument is complex and time-intensive. In this paper, we focus on applying contrastive learning approaches to a variety of remote sensing datasets. We show that Viewmaker networks, a recently proposed method for generating views, are promising for producing views in this setting without requiring extensive domain knowledge and trial and error. We apply Viewmaker to four multispectral imaging problems, each with a different format, finding that Viewmaker can outperform cropping- and reflection-based methods for contrastive learning in every case when evaluated on downstream classification tasks. This provides additional evidence that domain-agnostic methods can empower contrastive learning to scale to real-world scientific domains. Open source code can be found at https://github.com/jbayrooti/divmaker.

Does the use of auto-differentiation yield reasonable updates to deep neural networks that represent neural ODEs? Through mathematical analysis and numerical evidence, we find that when the neural network employs high-order forms to approximate the underlying ODE flows (such as the Linear Multistep Method (LMM)), brute-force computation using auto-differentiation often produces non-converging artificial oscillations. In the case of Leapfrog, we propose a straightforward post-processing technique that effectively eliminates these oscillations, rectifies the gradient computation and thus respects the updates of the underlying flow.

Space weather indices are used commonly to drive forecasts of thermosphere density, which directly affects objects in low-Earth orbit (LEO) through atmospheric drag. One of the most commonly used space weather proxies, $F_{10.7 cm}$, correlates well with solar extreme ultra-violet (EUV) energy deposition into the thermosphere. Currently, the USAF contracts Space Environment Technologies (SET), which uses a linear algorithm to forecast $F_{10.7 cm}$. In this work, we introduce methods using neural network ensembles with multi-layer perceptrons (MLPs) and long-short term memory (LSTMs) to improve on the SET predictions. We make predictions only from historical $F_{10.7 cm}$ values, but also investigate data manipulation to improve forecasting. We investigate data manipulation methods (backwards averaging and lookback) as well as multi step and dynamic forecasting. This work shows an improvement over the baseline when using ensemble methods. The best models found in this work are ensemble approaches using multi step or a combination of multi step and dynamic predictions. Nearly all approaches offer an improvement, with the best models improving between 45 and 55\% on relative MSE. Other relative error metrics were shown to improve greatly when ensembles methods were used. We were also able to leverage the ensemble approach to provide a distribution of predicted values; allowing an investigation into forecast uncertainty. Our work found models that produced less biased predictions at elevated and high solar activity levels. Uncertainty was also investigated through the use of a calibration error score metric (CES), our best ensemble reached similar CES as other work.

Ever since the discovery of x-rays, considerable breakthroughs have been made using them as a probe of matter, from testing models of the atom to solving the structure of deoxyribonucleic acid (DNA). Over the last few decades with the proliferation of synchrotron x-ray sources around the world, the application to many scientific fields has progressed tremendously and allowed studies of complicated structures and phenomena like protein dynamics and crystallography [1, 2], electronic structures of strongly correlated materials [3, 4], and a wide variety of elementary excitations [5, 6]. With the the development of the next generation of light sources, especially the x-ray free electron lasers (X-FEL) [7, 8], not only have discoveries accelerated, but completely novel techniques have been developed and new fields of science have emerged, such as laboratory astrophysics [9, 10, 11, 12] and single particle diffractive imaging [13, 14, 15]. Among these emerging techniques brought by X-FELs, the development of x-ray photon fluctuation spectroscopy (XPFS) holds particular relevance for condensed matter and material physics [16]. XPFS is a unique and powerful approach that opens up numerous opportunities to probe ultrafast dynamics of timescales corresponding to the µeV to meV-energy level. As the high-level coherence of the x-ray beam encodes subtle changes in the system at these timescales, XPFS is capable of investigating fluctuations of elementary excitations, such as that of the spin [17]. The fluctuation spectra collected using this method can be directly related back to correlation functions derived from Hamiltonians [18, 19], yielding invaluable experimental insights for theoretical developments and deeper understandings of the underlying physics.

To well understand crowd behavior, microscopic models have been developed in recent decades, in which an individual's behavioral/psychological status can be modeled and simulated. A well-known model is the social-force model innovated by physical scientists (Helbing and Molnar, 1995; Helbing, Farkas and Vicsek, 2000; Helbing et al., 2002). This model has been widely accepted and mainly used in simulation of crowd evacuation in the past decade. A problem, however, is that the testing results of the model were not explained in consistency with the psychological findings, resulting in misunderstanding of the model by psychologists. This paper will bridge the gap between psychological studies and physical explanation about this model. We reinterpret this physics-based model from a psychological perspective, clarifying that the model is consistent with psychological theories on stress, including time-related stress and interpersonal stress. Based on the conception of stress, we renew the model at both micro-and-macro level, referring to multi-agent simulation in a microscopic sense and fluid-based analysis in a macroscopic sense. The cognition and behavior of individual agents are critically modeled as response to environmental stimuli. Existing simulation results such as faster-is-slower effect will be reinterpreted by Yerkes-Dodson law, and herding and grouping effect as well as oscillation phenomenon are further discussed for pedestrian crowd. In brief the social-force model exhibits a bridge between the physics laws and psychological principles regarding crowd motion, and this paper will renew and reinterpret the model on the foundation of psychological studies.

The aim of this study is to develop and apply an autonomous approach for predicting the probability of hydrocarbon reservoirs spreading in the studied area. The methodology uses machine learning algorithms in the problem of binary classification, which restore the probability function of the space element belonging to the classes identified by the results of interpretation of well logging. Attributes of seismic wavefield are used as predictors. The study includes the following sequence of actions: creation of data sets for training, selection of features, reverse-calibration of data, creation of a population of classification models, evaluation of classification quality, evaluation of the contribution of features in the prediction, ensembling the population of models by stacking method. As a result, a prediction was made - a three-dimensional cube of calibrated probabilities of belonging of the studied space to the class of reservoir and its derivative in the form of the map of reservoir thicknesses of the Achimov complex of deposits was obtained. Assessment of changes in the quality of the forecast depending on the use of different data sets was carried out. Conclusion. The reverse-calibration method proposed in this work uses the uncertainty of geophysical data as a hyperparameter of the global tuning of the technological stack, within the given limits of the a priori error of these data. It is shown that the method improves the quality of the forecast. The technological stack of machine learning algorithms used in this work allows expert-independent generalization of geological and geophysical data, and use this generalization to test hypotheses and create geological models based on a probabilistic view of the reservoir.

Hit rate is a key performance metric in predicting process product quality in integrated industrial processes. It represents the percentage of products accepted by downstream processes within a controlled range of quality. However, optimizing hit rate is a non-convex and challenging problem. To address this issue, we propose a data-driven quasi-convex approach that combines factorial hidden Markov models, multitask elastic net, and quasi-convex optimization. Our approach converts the original non-convex problem into a set of convex feasible problems, achieving an optimal hit rate. We verify the convex optimization property and quasi-convex frontier through Monte Carlo simulations and real-world experiments in steel production. Results demonstrate that our approach outperforms classical models, improving hit rates by at least 41.11% and 31.01% on two real datasets. Furthermore, the quasi-convex frontier provides a reference explanation and visualization for the deterioration of solutions obtained by conventional models.