Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum unit price p. The market clears at the price at which the aggregate demand intersects the total supply and firms are paid the bid prices. We study a game theoretic model of competition among such firms and focus on its equilibria (Supply function equilibrium). The game we consider is a generalization of both models where firms can either set a fixed quantity (Cournot model) or set a fixed price (Bertrand model). Our main result is to prove existence and provide a characterization of (pure strategy) Nash equilibria in the space of K-Lipschitz supply functions.

Poisson's equation plays an important role in modeling many physical systems. In electrostatic self-consistent low-temperature plasma (LTP) simulations, Poisson's equation is solved at each simulation time step, which can amount to a significant computational cost for the entire simulation. In this paper, we describe the development of a generic machine-learned Poisson solver specifically designed for the requirements of LTP simulations in complex 2D reactor geometries on structured Cartesian grids. Here, the reactor geometries can consist of inner electrodes and dielectric materials as often found in LTP simulations. The approach leverages a hybrid CNN-transformer network architecture in combination with a weighted multiterm loss function. We train the network using highly-randomized synthetic data to ensure the generalizability of the learned solver to unseen reactor geometries. The results demonstrate that the learned solver is able to produce quantitatively and qualitatively accurate solutions. Furthermore, it generalizes well on new reactor geometries such as reference geometries found in the literature. To increase the numerical accuracy of the solutions required in LTP simulations, we employ a conventional iterative solver to refine the raw predictions, especially to recover the high-frequency features not resolved by the initial prediction. With this, the proposed learned Poisson solver provides the required accuracy and is potentially faster than a pure GPU-based conventional iterative solver. This opens up new possibilities for developing a generic and high-performing learned Poisson solver for LTP systems in complex geometries.

Multi-agent reinforcement learning (MARL) models multiple agents that interact and learn within a shared environment. This paradigm is applicable to various industrial scenarios such as autonomous driving, quantitative trading, and inventory management. However, applying MARL to these real-world scenarios is impeded by many challenges such as scaling up, complex agent interactions, and non-stationary dynamics. To incentivize the research of MARL on these challenges, we develop MABIM (Multi-Agent Benchmark for Inventory Management) which is a multi-echelon, multi-commodity inventory management simulator that can generate versatile tasks with these different challenging properties. Based on MABIM, we evaluate the performance of classic operations research (OR) methods and popular MARL algorithms on these challenging tasks to highlight their weaknesses and potential.

Graph neural networks are among the most successful machine learning models for relational datasets like metabolic, transportation, and social networks. Yet the determinants of their strong generalization for diverse interactions encoded in the data are not well understood. Methods from statistical learning theory do not explain emergent phenomena such as double descent or the dependence of risk on the nature of interactions. We use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. The derived curves are phenomenologically rich: they explain the distinction between learning on homophilic and heterophilic and they predict double descent whose existence in GNNs has been questioned by recent work. We show how risk depends on the interplay between the noise in the graph, noise in the features, and the proportion of nodes used for training. Our analysis predicts qualitative behavior not only of a stylized graph learning model but also to complex GNNs on messy real-world datasets. As a case in point, we use these analytic insights about heterophily and self-loop signs to improve performance of state-of-the-art graph convolution networks on several heterophilic benchmarks by a simple addition of negative self-loop filters.

Solar panels on Earth already provide us with a clean source of power, but they can be a blot on the landscape and are practically useless when it's dark. Now, scientists in California have provided a solution – sending solar panels to space so they can harness the sun's power 24/7. In a world first, the researchers beamed solar energy to Earth from a spacecraft called MAPLE, which was launched to orbit in January. MAPLE is equipped with solar panels that can withstand'the harsh environment of space', including wild temperature swings and solar radiation. 'Space solar power' – a concept conjured by science-fiction writer Isaac Asimov in 1941 – could potentially yield eight times more power than solar panels at any location on Earth's surface.

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase unceasingly. This growth of the deep learning models is accompanied by issues related to their considerable energy consumption, both during the training and inference phases, as well as their scalability. Although a number of work based on unconventional physical systems have been proposed which addresses the issue of energy efficiency in the inference phase, efficient training of deep learning models has remained unaddressed. So far, training of digital deep learning models mainly relies on backpropagation, which is not suitable for physical implementation as it requires perfect knowledge of the computation performed in the so-called forward pass of the neural network. Here, we tackle this issue by proposing a simple deep neural network architecture augmented by a biologically plausible learning algorithm, referred to as "model-free forward-forward training". The proposed architecture enables training deep physical neural networks consisting of layers of physical nonlinear systems, without requiring detailed knowledge of the nonlinear physical layers' properties. We show that our method outperforms state-of-the-art hardware-aware training methods by improving training speed, decreasing digital computations, and reducing power consumption in physical systems. We demonstrate the adaptability of the proposed method, even in systems exposed to dynamic or unpredictable external perturbations. To showcase the universality of our approach, we train diverse wave-based physical neural networks that vary in the underlying wave phenomenon and the type of non-linearity they use, to perform vowel and image classification tasks experimentally.

When making strategic decisions, we are often confronted with overwhelming information to process. The situation can be further complicated when some pieces of evidence are contradicted each other or paradoxical. The challenge then becomes how to determine which information is useful and which ones should be eliminated. This process is known as meta-decision. Likewise, when it comes to using Artificial Intelligence (AI) systems for strategic decision-making, placing trust in the AI itself becomes a meta-decision, given that many AI systems are viewed as opaque "black boxes" that process large amounts of data. Trusting an opaque system involves deciding on the level of Trustworthy AI (TAI). We propose a new approach to address this issue by introducing a novel taxonomy or framework of TAI, which encompasses three crucial domains: articulate, authentic, and basic for different levels of trust. To underpin these domains, we create ten dimensions to measure trust: explainability/transparency, fairness/diversity, generalizability, privacy, data governance, safety/robustness, accountability, reproducibility, reliability, and sustainability. We aim to use this taxonomy to conduct a comprehensive survey and explore different TAI approaches from a strategic decision-making perspective.

Zero-shot detection (ZSD), i.e., detection on classes not seen during training, is essential for real world detection use-cases, but remains a difficult task. Recent research attempts ZSD with detection models that output embeddings instead of direct class labels. To this aim, the output of the detection model must be aligned to a learned embedding space such as CLIP. However, this alignment is hindered by detection data sets which are expensive to produce compared to image classification annotations, and the resulting lack of category diversity in the training data. We address this challenge by leveraging the CLIP embedding space in combination with image labels from ImageNet. Our results show that image labels are able to better align the detector output to the embedding space and thus have a high potential for ZSD. Compared to only training on detection data, we see a significant gain by adding image label data of 3.3 mAP for the 65/15 split on COCO on the unseen classes, i.e., we more than double the gain of related work.

With rapid progress in deep learning, neural networks have been widely used in scientific research and engineering applications as surrogate models. Despite the great success of neural networks in fitting complex systems, two major challenges still remain: i) the lack of generalization on different problems/datasets, and ii) the demand for large amounts of simulation data that are computationally expensive. To resolve these challenges, we propose the differentiable \mf (DMF) model, which leverages neural architecture search (NAS) to automatically search the suitable model architecture for different problems, and transfer learning to transfer the learned knowledge from low-fidelity (fast but inaccurate) data to high-fidelity (slow but accurate) model. Novel and latest machine learning techniques such as hyperparameters search and alternate learning are used to improve the efficiency and robustness of DMF. As a result, DMF can efficiently learn the physics simulations with only a few high-fidelity training samples, and outperform the state-of-the-art methods with a significant margin (with up to 58$\%$ improvement in RMSE) based on a variety of synthetic and practical benchmark problems.

Graphene is one of the most researched two dimensional (2D) material due to its unique combination of mechanical, thermal and electrical properties. Special 2D structure of graphene enables it to exhibit a wide range of peculiar material properties like high Young's modulus, high specific strength etc. which are critical for myriad of applications including light weight structural materials, multi-functional coating and flexible electronics. It is quite challenging and costly to experimentally investigate graphene/graphene based nanocomposites, computational simulations such as molecular dynamics (MD) simulations are widely adopted for understanding the microscopic origins of their unique properties. However, disparate results were reported from computational studies, especially MD simulations using various empirical inter-atomic potentials. In this work, an artificial neural network based interatomic potential has been developed for graphene to represent the potential energy surface based on first principle calculations. The developed machine learning potential (MLP) facilitates high fidelity MD simulations to approach the accuracy of ab initio methods but with a fraction of computational cost, which allows larger simulation size/length, and thereby enables accelerated discovery/design of graphene-based novel materials. Lattice parameter, coefficient of thermal expansion (CTE), Young's modulus and yield strength are estimated using machine learning accelerated MD simulations (MLMD), which are compared to experimental/first principle calculations from previous literatures. It is demonstrated that MLMD can capture the dominating mechanism governing CTE of graphene, including effects from lattice parameter and out of plane rippling.