This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered Large Eddy Simulation (LES). Here, the induced filter kernel, and thus the closure terms, are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with Reinforcement Learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and Finite Volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.

The optimization of well locations and controls is an important step in the design of subsurface flow operations such as oil production or geological CO2 storage. These optimization problems can be computationally expensive, however, as many potential candidate solutions must be evaluated. In this study, we propose a graph network surrogate model (GNSM) for optimizing well placement and controls. The GNSM transforms the flow model into a computational graph that involves an encoding-processing-decoding architecture. Separate networks are constructed to provide global predictions for the pressure and saturation state variables. Model performance is enhanced through the inclusion of the single-phase steady-state pressure solution as a feature. A multistage multistep strategy is used for training. The trained GNSM is applied to predict flow responses in a 2D unstructured model of a channelized reservoir. Results are presented for a large set of test cases, in which five injection wells and five production wells are placed randomly throughout the model, with a random control variable (bottom-hole pressure) assigned to each well. Median relative error in pressure and saturation for 300 such test cases is 1-2%. The ability of the trained GNSM to provide accurate predictions for a new (geologically similar) permeability realization is demonstrated. Finally, the trained GNSM is used to optimize well locations and controls with a differential evolution algorithm. GNSM-based optimization results are comparable to those from simulation-based optimization, with a runtime speedup of a factor of 36. Much larger speedups are expected if the method is used for robust optimization, in which each candidate solution is evaluated on multiple geological models.

Reinforcement Learning from Human Feedback (RLHF) has shown potential in qualitative tasks where clear objectives are lacking. However, its effectiveness is not fully realized when it is conceptualized merely as a tool to optimize average human preferences, especially in generative tasks that demand diverse model responses. Meanwhile, Quality Diversity (QD) algorithms excel at identifying diverse and high-quality solutions but often rely on manually crafted diversity metrics. This paper introduces Quality Diversity through Human Feedback (QDHF), a novel approach integrating human feedback into the QD framework. QDHF infers diversity metrics from human judgments of similarity among solutions, thereby enhancing the applicability and effectiveness of QD algorithms. Our empirical studies show that QDHF significantly outperforms state-of-the-art methods in automatic diversity discovery and matches the efficacy of using manually crafted metrics for QD on standard benchmarks in robotics and reinforcement learning. Notably, in a latent space illumination task, QDHF substantially enhances the diversity in images generated by a diffusion model and was more favorably received in user studies. We conclude by analyzing QDHF's scalability and the quality of its derived diversity metrics, emphasizing its potential to improve exploration and diversity in complex, open-ended optimization tasks. Source code is available on GitHub: https://github.com/ld-ing/qdhf.

Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and systems biology. Its weighted variant named minimum weight connected dominating set is also useful in such applications. In this paper, we propose a simulated annealing algorithm based on a greedy heuristic for tackling a variant of the minimum connected dominating set problem and that by exploiting two objectives together namely the cardinality and the total weight of the connected dominating set. Experimental results compared to those obtained by a recent proposed research show the superiority of our approach.

Learning-based approaches for controlling safety-critical systems are rapidly growing in popularity; thus, it is important to assure their performance and safety. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing such guarantees, since it can handle general nonlinear system dynamics, bounded adversarial system disturbances, and state and input constraints. However, its computational and memory complexity scales exponentially with the state dimension, making it intractable for large-scale systems. To overcome this challenge, neural approaches, such as DeepReach, have been used to synthesize reachable tubes and safety controllers for high-dimensional systems. However, verifying these neural reachable tubes remains challenging. In this work, we propose two verification methods, based on robust scenario optimization and conformal prediction, to provide probabilistic safety guarantees for neural reachable tubes. Our methods allow a direct trade-off between resilience to outlier errors in the neural tube, which are inevitable in a learning-based approach, and the strength of the probabilistic safety guarantee. Furthermore, we show that split conformal prediction, a widely used method in the machine learning community for uncertainty quantification, reduces to a scenario-based approach, making the two methods equivalent not only for verification of neural reachable tubes but also more generally. To our knowledge, our proof is the first in the literature to show a strong relationship between conformal prediction and scenario optimization. Finally, we propose an outlier-adjusted verification approach that uses the error distribution in neural reachable tubes to recover greater safe volumes. We demonstrate the efficacy of the proposed approaches for the high-dimensional problems of multi-vehicle collision avoidance and rocket landing with no-go zones.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical framework that efficiently scales toward large-scale routing problems. GLOP partitions large routing problems into Travelling Salesman Problems (TSPs) and TSPs into Shortest Hamiltonian Path Problems. For the first time, we hybridize non-autoregressive neural heuristics for coarse-grained problem partitions and autoregressive neural heuristics for fine-grained route constructions, leveraging the scalability of the former and the meticulousness of the latter. Experimental results show that GLOP achieves competitive and state-of-the-art real-time performance on large-scale routing problems, including TSP, ATSP, CVRP, and PCTSP.

Federated Learning (FL) is a distributed machine learning paradigm that addresses privacy concerns in machine learning and still guarantees high test accuracy. However, achieving the necessary accuracy by having all clients participate in FL is impractical, given the constraints of client local computing resource. In this paper, we introduce a multi-user collaborative computing framework, categorizing users into two roles: model owners (MOs) and data owner (DOs). Without resorting to monetary incentives, an MO can encourage more DOs to join in FL by allowing the DOs to offload extra local computing tasks to the MO for execution. This exchange of "data" for "computing resources" streamlines the incentives for clients to engage more effectively in FL. We formulate the interaction between MO and DOs as an optimization problem, and the objective is to effectively utilize the communication and computing resource of the MO and DOs to minimize the time to complete an FL task. The proposed problem is a mixed integer nonlinear programming (MINLP) with high computational complexity. We first decompose it into two distinct subproblems, namely the client selection problem and the resource allocation problem to segregate the integer variables from the continuous variables. Then, an effective iterative algorithm is proposed to solve problem. Simulation results demonstrate that the proposed collaborative computing framework can achieve an accuracy of more than 95\% while minimizing the overall time to complete an FL task.

This paper proposes a blockchain-secured deep reinforcement learning (BC-DRL) optimization framework for {data management and} resource allocation in decentralized {wireless mobile edge computing (MEC)} networks. In our framework, {we design a low-latency reputation-based proof-of-stake (RPoS) consensus protocol to select highly reliable blockchain-enabled BSs to securely store MEC user requests and prevent data tampering attacks.} {We formulate the MEC resource allocation optimization as a constrained Markov decision process that balances minimum processing latency and denial-of-service (DoS) probability}. {We use the MEC aggregated features as the DRL input to significantly reduce the high-dimensionality input of the remaining service processing time for individual MEC requests. Our designed constrained DRL effectively attains the optimal resource allocations that are adapted to the dynamic DoS requirements. We provide extensive simulation results and analysis to} validate that our BC-DRL framework achieves higher security, reliability, and resource utilization efficiency than benchmark blockchain consensus protocols and {MEC} resource allocation algorithms.

Research on adversarial robustness is primarily focused on image and text data. Yet, many scenarios in which lack of robustness can result in serious risks, such as fraud detection, medical diagnosis, or recommender systems often do not rely on images or text but instead on tabular data. Adversarial robustness in tabular data poses two serious challenges. First, tabular datasets often contain categorical features, and therefore cannot be tackled directly with existing optimization procedures. Second, in the tabular domain, algorithms that are not based on deep networks are widely used and offer great performance, but algorithms to enhance robustness are tailored to neural networks (e.g. adversarial training). In this paper, we tackle both challenges. We present a method that allows us to train adversarially robust deep networks for tabular data and to transfer this robustness to other classifiers via universal robust embeddings tailored to categorical data. These embeddings, created using a bilevel alternating minimization framework, can be transferred to boosted trees or random forests making them robust without the need for adversarial training while preserving their high accuracy on tabular data. We show that our methods outperform existing techniques within a practical threat model suitable for tabular data.