In model-based reinforcement learning, most algorithms rely on simulating trajectories from one-step models of the dynamics learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as the length of the trajectory grows. In this paper we tackle this issue by using a multi-step objective to train one-step models. Our objective is a weighted sum of the mean squared error (MSE) loss at various future horizons. We find that this new loss is particularly useful when the data is noisy (additive Gaussian noise in the observations), which is often the case in real-life environments. To support the multi-step loss, first we study its properties in two tractable cases: i) uni-dimensional linear system, and ii) two-parameter non-linear system. Second, we show in a variety of tasks (environments or datasets) that the models learned with this loss achieve a significant improvement in terms of the averaged R2-score on future prediction horizons. Finally, in the pure batch reinforcement learning setting, we demonstrate that one-step models serve as strong baselines when dynamics are deterministic, while multi-step models would be more advantageous in the presence of noise, highlighting the potential of our approach in real-world applications.

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in converging to solutions of highly nonlinear parametric-PDEs like NSE. We consider the parameter(s) of interest as inputs of PINNs along with spatio-temporal coordinates, and train PINNs on generated numerical solutions of parametric-PDES for instances of the parameters. We perform experiments on the classical 2D flow past cylinder problem aiming to learn velocities and pressure functions over a range of Reynolds numbers as parameter of interest. Provision of training data from generated numerical simulations allows for interpolation of the solution functions for a range of parameters. Therefore, we compare PINNs with unconstrained conventional Neural Networks (NN) on this problem setup to investigate the effectiveness of considering the PDEs regularization in the loss function. We show that our proposed approach results in optimizing PINN models that learn the solution functions while making sure that flow predictions are in line with conservational laws of mass and momentum. Our results show that PINN results in accurate prediction of gradients compared to NN model, this is clearly visible in predicted vorticity fields given that none of these models were trained on vorticity labels.

Whether embedding spaces use all their dimensions equally, i.e., whether they are isotropic, has been a recent subject of discussion. Evidence has been accrued both for and against enforcing isotropy in embedding spaces. In the present paper, we stress that isotropy imposes requirements on the embedding space that are not compatible with the presence of clusters -- which also negatively impacts linear classification objectives. We demonstrate this fact empirically and use it to shed light on previous results from the literature.

The paper presents the exact formula for the vector field that minimizes the loss for the standard flow. This formula depends analytically on a given distribution \rho_0 and an unknown one \rho_1. Based on the presented formula, a new loss and algorithm for training a vector field model in the style of Conditional Flow Matching are provided. Our loss, in comparison to the standard Conditional Flow Matching approach, exhibits smaller variance when evaluated through Monte Carlo sampling methods. Numerical experiments on synthetic models and models on tabular data of large dimensions demonstrate better learning results with the use of the presented algorithm.

Black-box optimization has emerged as an effective technique in many real-world applications to find the global optimum of expensive, noisy black-box functions. Some notable applications include hyper-parameter optimization in machine learning algorithms Snoek et al. [2012], Bergstra and Bengio [2012], synthesis of short polymer fiber materials, alloy design, 3D bio-printing, and molecule design Greenhill et al. [2020], Shahriari et al. [2015], optimizing design parameters in computational fluid dynamics Morita et al. [2022], and scientific research (e.g., multilayer nanoparticle, photonic crystal topology) Kim et al. [2022]. Bayesian Optimization is a popular example of black-box optimization method. Typically, Bayesian Optimization algorithms use a probabilistic regression model, such as a Gaussian Process (GP), trained on existing function observations. This model is then utilized to create an acquisition function that balances exploration and exploitation to recommend the next evaluation point for the black-box functions. Various options exist for acquisition functions, including improvement-based methods like Probability of Improvement Kushner [1964], Expected Improvement Mockus et al. [1978], the Upper Confidence Bound Srinivas

This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator (GPWNO), which operates in the infinite-dimensional functional space using the plane-wave and Gaussian-type orbital bases, widely recognized in the context of DFT. In particular, both high- and low-frequency components of the density can be effectively represented due to the complementary nature of the two bases. Extensive experiments on QM9, MD, and material project datasets demonstrate GPWNO's superior performance over ten baselines.

The availability of large, public, multi-modal astronomical datasets presents an opportunity to execute novel research that straddles the line between science of AI and science of astronomy. Photometric redshift estimation is a well-established subfield of astronomy. Prior works show that computer vision models typically outperform catalog-based models, but these models face additional complexities when incorporating images from more than one instrument or sensor. In this report, we detail our progress creating Mantis Shrimp, a multi-survey computer vision model for photometric redshift estimation that fuses ultra-violet (GALEX), optical (PanSTARRS), and infrared (UnWISE) imagery. We use deep learning interpretability diagnostics to measure how the model leverages information from the different inputs. We reason about the behavior of the CNNs from the interpretability metrics, specifically framing the result in terms of physically-grounded knowledge of galaxy properties.

We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution. Moreover, LJLs are embedded in the generation process of point cloud networks by adding them at later stages of the inference process. The improvements in 3D point cloud generation utilizing LJLs are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural network.

Despite deep learning's widespread success, its data-hungry and computationally expensive nature makes it impractical for many data-constrained real-world applications. Few-Shot Learning (FSL) aims to address these limitations by enabling rapid adaptation to novel learning tasks, seeing significant growth in recent years. This survey provides a comprehensive overview of the field's latest advancements. Initially, FSL is formally defined, and its relationship with different learning fields is presented. A novel taxonomy is introduced, extending previously proposed ones, and real-world applications in classic and novel fields are described. Finally, recent trends shaping the field, outstanding challenges, and promising future research directions are discussed.

Foundation models have indeed made a profound impact on various fields, emerging as pivotal components that significantly shape the capabilities of intelligent systems. In the context of intelligent vehicles, leveraging the power of foundation models has proven to be transformative, offering notable advancements in visual understanding. Equipped with multi-modal and multi-task learning capabilities, multi-modal multi-task visual understanding foundation models (MM-VUFMs) effectively process and fuse data from diverse modalities and simultaneously handle various driving-related tasks with powerful adaptability, contributing to a more holistic understanding of the surrounding scene. In this survey, we present a systematic analysis of MM-VUFMs specifically designed for road scenes. Our objective is not only to provide a comprehensive overview of common practices, referring to task-specific models, unified multi-modal models, unified multi-task models, and foundation model prompting techniques, but also to highlight their advanced capabilities in diverse learning paradigms. These paradigms include open-world understanding, efficient transfer for road scenes, continual learning, interactive and generative capability. Moreover, we provide insights into key challenges and future trends, such as closed-loop driving systems, interpretability, embodied driving agents, and world models. To facilitate researchers in staying abreast of the latest developments in MM-VUFMs for road scenes, we have established a continuously updated repository at https://github.com/rolsheng/MM-VUFM4DS