Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural operators is still data-driven, which needs an expensive ground-truth dataset from various sources (e.g., solving PDEs' samples with the conventional solvers, real-world experiments) in addition to training stage costs. From a computational perspective, marrying operator learning and specific domain knowledge to solve PDEs is an essential step in reducing dataset costs and label-free learning. We propose a novel paradigm that provides a unified framework of training neural operators and solving PDEs with the variational form, which we refer to as the variational operator learning (VOL). Ritz and Galerkin approach with finite element discretization are developed for VOL to achieve matrix-free approximation of system functional and residual, then direct minimization and iterative update are proposed as two optimization strategies for VOL. Various types of experiments based on reasonable benchmarks about variable heat source, Darcy flow, and variable stiffness elasticity are conducted to demonstrate the effectiveness of VOL. With a label-free training set and a 5-label-only shift set, VOL learns solution operators with its test errors decreasing in a power law with respect to the amount of unlabeled data. To the best of the authors' knowledge, this is the first study that integrates the perspectives of the weak form and efficient iterative methods for solving sparse linear systems into the end-to-end operator learning task.

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane generator mapping the problem data and previous iterates to cutting planes. We propose a CPL implementation to generate split cuts, and by combining several CPLs, we devise a differentiable cutting-plane algorithm that exploits the repeated nature of parametric instances. In an offline phase, we train our algorithm by updating the internal parameters controlling the CPLs, thus altering cut generation. Once trained, our algorithm computes, with predictable execution times and a fixed number of cuts, solutions with low integrality gaps. Preliminary computational tests show that our algorithm generalizes on unseen instances and captures underlying parametric structures.

Mapping forest resources and carbon is important for improving forest management and meeting the objectives of storing carbon and preserving the environment. Spaceborne remote sensing approaches have considerable potential to support forest height monitoring by providing repeated observations at high spatial resolution over large areas. This study uses a machine learning approach that was previously developed to produce local maps of forest parameters (basal area, height, diameter, etc.). The aim of this paper is to present the extension of the approach to much larger scales such as the French national coverage. We used the GEDI Lidar mission as reference height data, and the satellite images from Sentinel-1, Sentinel-2 and ALOS-2 PALSA-2 to estimate forest height and produce a map of France for the year 2020. The height map is then derived into volume and aboveground biomass (AGB) using allometric equations. The validation of the height map with local maps from ALS data shows an accuracy close to the state of the art, with a mean absolute error (MAE) of 4.3 m. Validation on inventory plots representative of French forests shows an MAE of 3.7 m for the height. Estimates are slightly better for coniferous than for broadleaved forests. Volume and AGB maps derived from height shows MAEs of 75 tons/ha and 93 m${}^3$/ha respectively. The results aggregated by sylvo-ecoregion and forest types (owner and species) are further improved, with MAEs of 23 tons/ha and 30 m${}^3$/ha. The precision of these maps allows to monitor forests locally, as well as helping to analyze forest resources and carbon on a territorial scale or on specific types of forests by combining the maps with geolocated information (administrative area, species, type of owner, protected areas, environmental conditions, etc.). Height, volume and AGB maps produced in this study are made freely available.

Neural networks have shown remarkable performance in computer vision, but their deployment in numerous scientific and technical fields is challenging due to their black-box nature. Scientists and practitioners need to evaluate the reliability of a decision, i.e., to know simultaneously if a model relies on the relevant features and whether these features are robust to image corruptions. Existing attribution methods aim to provide human-understandable explanations by highlighting important regions in the image domain, but fail to fully characterize a decision process's reliability. To bridge this gap, we introduce the Wavelet sCale Attribution Method (WCAM), a generalization of attribution from the pixel domain to the space-scale domain using wavelet transforms. Attribution in the wavelet domain reveals where and on what scales the model focuses, thus enabling us to assess whether a decision is reliable.

Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing provably valid confidence intervals for quantities such as means, quantiles, and linear and logistic regression coefficients, without making any assumptions on the machine-learning algorithm that supplies the predictions. Furthermore, more accurate predictions translate to smaller confidence intervals. Prediction-powered inference could enable researchers to draw valid and more data-efficient conclusions using machine learning. The benefits of prediction-powered inference are demonstrated with datasets from proteomics, astronomy, genomics, remote sensing, census analysis, and ecology.

If you look at the UN Sustainable Development Goals, it's clear that robots have a huge role to play in advancing the SDGs. However the field of Sustainable Robotics is more than just the application area. For every application that robotics can improve in sustainability, you have to also address the question – what are the additional costs or benefits all the way along the supply chain. What are the'externalities', or additional costs/benefits, of using robots to solve the problem. Solving our economic and environmental global challenges should not involve adding to the existing problems or creating new ones.

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH; and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

Planning robot dexterity is challenging due to the non-smoothness introduced by contacts, intricate fine motions, and ever-changing scenarios. We present a hierarchical planning framework for dexterous robotic manipulation (HiDex). This framework explores in-hand and extrinsic dexterity by leveraging contacts. It generates rigid-body motions and complex contact sequences. Our framework is based on Monte-Carlo Tree Search and has three levels: 1) planning object motions and environment contact modes; 2) planning robot contacts; 3) path evaluation and control optimization. This framework offers two main advantages. First, it allows efficient global reasoning over high-dimensional complex space created by contacts. It solves a diverse set of manipulation tasks that require dexterity, both intrinsic (using the fingers) and extrinsic (also using the environment), mostly in seconds. Second, our framework allows the incorporation of expert knowledge and customizable setups in task mechanics and models. It requires minor modifications to accommodate different scenarios and robots. Hence, it provides a flexible and generalizable solution for various manipulation tasks. As examples, we analyze the results on 7 hand configurations and 15 scenarios. We demonstrate 8 tasks on two robot platforms.

In this study, we have developed a dynamic asset allocation investment strategy using reinforcement learning techniques. To begin with, we have addressed the crucial issue of incorporating non-stationarity of financial time series data into reinforcement learning algorithms, which is a significant implementation in the application of reinforcement learning in investment strategies. Our findings highlight the significance of introducing certain variables such as regime change in the environment setting to enhance the prediction accuracy. Furthermore, the application of reinforcement learning in investment strategies provides a remarkable advantage of setting the optimization problem flexibly. This enables the integration of practical constraints faced by investors into the algorithm, resulting in efficient optimization. Our study has categorized the investment strategy formulation conditions into three main categories, including performance measurement indicators, portfolio management rules, and other constraints. We have evaluated the impact of incorporating these conditions into the environment and rewards in a reinforcement learning framework and examined how they influence investment behavior.

Fluid interactions permeate daily human activities, with properties like density and viscosity playing pivotal roles in household tasks. While density estimation is straightforward through Archimedes' principle, viscosity poses a more intricate challenge, especially given the varied behaviors of Newtonian and non-Newtonian fluids. These fluids, which differ in their stress-strain relationships, are delineated by specific constitutive models such as the Carreau, Cross, and Herschel-Bulkley models, each possessing unique viscosity parameters. This study introduces a novel differentiable fitting framework, DiffStir, tailored to identify key physics parameters via the common daily operation of stirring. By employing a robotic arm for stirring and harnessing a differentiable Material Point Method (diffMPM)-based simulator, the framework can determine fluid parameters by matching observations from both the simulator and the real world. Recognizing the distinct preferences of the aforementioned constitutive models for specific fluids, an online strategy was adopted to adaptively select the most fitting model based on real-world data. Additionally, we propose a refining neural network to bridge the sim-to-real gap and mitigate sensor noise-induced inaccuracies. Comprehensive experiments were conducted to validate the efficacy of DiffStir, showcasing its precision in parameter estimation when benchmarked against reported literature values. More experiments and videos can be found in the supplementary materials and on the website: https://sites.google.com/view/diffstir.