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In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcome this training issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems, they do not always scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables. Our experiments verify the computational advantage our proposed method enjoys on two representative problems, namely the shortest path problem and the knapsack problem.

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.

Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a comprehensive overview of our research combining Machine Learning (ML) and Fraunhofer's MESHFREE software (www.meshfree.eu), a powerful tool utilizing a numerical point cloud in a Generalized Finite Difference Method (GFDM). This tool enables the effective handling of complex flow domains, moving geometries, and free surfaces, while allowing users to finely tune local refinement and quality parameters for an optimal balance between computation time and results accuracy. However, manually determining the optimal parameter combination poses challenges, especially for less experienced users. We introduce a novel ML-optimized approach, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time. This research contributes valuable insights into parameter optimization in meshfree simulations, enhancing accessibility and usability for a broader user base in scientific and engineering applications.

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve training efficiency and to enable control of the approximation error, the network mimics an adaptive finite element method (AFEM). It outputs a coarse grid solution and a series of corrections as produced in an AFEM, allowing a tracking of the error decay over successive layers of the network. The observed errors are measured by a reliable residual based a posteriori error estimator, enabling the reduction to only few parameters for the approximation in the output of the network. This leads to a problem adapted representation of the solution on locally refined grids. Furthermore, each solution of the AFEM is discretized in a hierarchical basis. For the architecture, convolutional neural networks (CNNs) are chosen. The hierarchical basis then allows to handle sparse images for finely discretized meshes. Additionally, as corrections on finer levels decrease in amplitude, i.e., importance for the overall approximation, the accuracy of the network approximation is allowed to decrease successively. This can either be incorporated in the number of generated high fidelity samples used for training or the size of the network components responsible for the fine grid outputs. The architecture is described and preliminary numerical examples are presented.

Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse of dimensionality when learning from high-dimensional data, the inherent reflectional and rotational symmetry of robot structures has not been adequately explored. Drawing inspiration from cooperative multi-agent reinforcement learning, we introduce novel network structures for single-agent control learning that explicitly capture these symmetries. Moreover, we investigate the relationship between the geometric prior and the concept of Parameter Sharing in multi-agent reinforcement learning. Last but not the least, we implement the proposed framework in online and offline learning methods to demonstrate its ease of use. Through experiments conducted on various challenging continuous control tasks on simulators and real robots, we highlight the significant potential of the proposed geometric regularity in enhancing robot learning capabilities.

In offline reinforcement learning (RL), an RL agent learns to solve a task using only a fixed dataset of previously collected data. While offline RL has been successful in learning real-world robot control policies, it typically requires large amounts of expert-quality data to learn effective policies that generalize to out-of-distribution states. Unfortunately, such data is often difficult and expensive to acquire in real-world tasks. Several recent works have leveraged data augmentation (DA) to inexpensively generate additional data, but most DA works apply augmentations in a random fashion and ultimately produce highly suboptimal augmented experience. In this work, we propose Guided Data Augmentation (GuDA), a human-guided DA framework that generates expert-quality augmented data. The key insight behind GuDA is that while it may be difficult to demonstrate the sequence of actions required to produce expert data, a user can often easily characterize when an augmented trajectory segment represents progress toward task completion. Thus, a user can restrict the space of possible augmentations to automatically reject suboptimal augmented data. To extract a policy from GuDA, we use off-the-shelf offline reinforcement learning and behavior cloning algorithms. We evaluate GuDA on a physical robot soccer task as well as simulated D4RL navigation tasks, a simulated autonomous driving task, and a simulated soccer task. Empirically, GuDA enables learning given a small initial dataset of potentially suboptimal experience and outperforms a random DA strategy as well as a model-based DA strategy.

This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing angle constraints on thrust vectors. This issue has been conventionally circumvented via lossless convexification (LCvx), which lifts a nonconvex feasible set to a higher-dimensional convex set, and via linear approximation of another nonconvex feasible set defined by exponential functions. However, this approach sometimes results in an infeasible solution when the solution obtained from the higher-dimensional space is projected back to the original space, especially when the problem involves a nonoptimal time of flight. Additionally, the Taylor series approximation introduces an approximation error that grows with both flight time and deviation from the reference trajectory. In this paper, we introduce a first-order approach that makes use of orthogonal projections onto nonconvex sets, allowing expansive projection (ExProj). We show that 1) this approach produces a feasible solution with better performance even for the nonoptimal time of flight cases for which conventional techniques fail to generate achievable trajectories and 2) the proposed method compensates for the linearization error that arises from Taylor series approximation, thus generating a superior guidance solution with less fuel consumption. We provide numerical examples featuring quantitative assessments to elucidate the effectiveness of the proposed methodology, particularly in terms of fuel consumption and flight time. Our analysis substantiates the assertion that the proposed approach affords enhanced flexibility in devising viable trajectories for a diverse array of planetary soft landing scenarios.

Outflow boundaries play an important role in multiphase fluid dynamics simulations that involve transition between liquid and vapor phases. These flows are dominated by low Weber numbers and a sharp jump in pressure, velocity, and temperature. Inadequate treatment of these jumps at the outlet generates undesirable fluid disturbances that propagate upstream and lead to instabilities within the computational domain. To mitigate these disturbances, we introduce a forcing term that can be applied to incompressible Navier-Stokes equations to enforce stability in the numerical solution. The forcing term acts as a damping mechanism to control vortices that are generated by droplet/bubbles in multiphase flows, and is designed to be a general formulation that can be coupled with a fixed pressure outflow boundary condition to simulate a variety of multiphase flow problems. We demonstrate its applicability to simulate pool and flow boiling problems, where bubble-induced vortices during evaporation and condensation present a challenge at the outflow. Validation and verification cases are chosen to quantify accuracy and stability of the proposed method in comparison to established benchmarks and reference solutions, along with detailed performance analysis for three-dimensional simulations on leadership supercomputing platforms. Computational experiments are performed using Flash-X, which is a composable open-source software instrument designed for multiscale fluid dynamics simulations on heterogeneous architectures.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

We propose a new method for event extraction (EE) task based on an imitation learning framework, specifically, inverse reinforcement learning (IRL) via generative adversarial network (GAN). The GAN estimates proper rewards according to the difference between the actions committed by the expert (or ground truth) and the agent among complicated states in the environment. EE task benefits from these dynamic rewards because instances and labels yield to various extents of difficulty and the gains are expected to be diverse -- e.g., an ambiguous but correctly detected trigger or argument should receive high gains -- while the traditional RL models usually neglect such differences and pay equal attention on all instances. Moreover, our experiments also demonstrate that the proposed framework outperforms state-of-the-art methods, without explicit feature engineering.