However, the solution of parametrized, time-dependent systems of partial differential equations (PDEs) by means of full order models (FOMs) - such as the finite element method - may clash with time and computational budget restrictions. Moreover, using FOMs to explore different scenarios with varying initial conditions and parameter combinations might be a computationally prohibitive task, or even infeasible in several practical applications. Differently from the problem of estimating output quantities of interest that depend on the solution of the differential problem, the computation of the whole solution field is intrinsically high-dimensional, with additional difficulties related to the nonlinear and time-dependent nature of the problem. All these reasons drive the search of efficient, but accurate, reduced order models (ROMs). Among these, the reduced basis method [56, 33, 4] is a very well-known approach, exploiting, e.g., proper orthogonal decomposition (POD) to build a reduced space, either global or local [1, 55], to approximate the solution of the problem. However, despite their accuracy and mathematical, these techniques are in general intrusive [25]. Among machine and deep learning techniques widely used to build surrogate models or emulators to the solution of parametrized, nonlinear, time-dependent system of PDEs, autoencoder (AE) neural networks [27] have recently become a popular strategy because they allow to non-intrusively reduce dimensionality and unveil latent features directly from data streams, without accessing the FOM operators [26, 43, 48, 37]. Their success is due to the expressiveness capacity of neural networks [11, 44, 34], which enables outstanding performances in nonlinear compression and great flexibility in identifying coordinate transformations [46].

Data selection is essential for any data-based optimization technique, such as Reinforcement Learning. State-of-the-art sampling strategies for the experience replay buffer improve the performance of the Reinforcement Learning agent. However, they do not incorporate uncertainty in the Q-Value estimation. Consequently, they cannot adapt the sampling strategies, including exploration and exploitation of transitions, to the complexity of the task. To address this, this paper proposes a new sampling strategy that leverages the exploration-exploitation trade-off. This is enabled by the uncertainty estimation of the Q-Value function, which guides the sampling to explore more significant transitions and, thus, learn a more efficient policy. Experiments on classical control environments demonstrate stable results across various environments. They show that the proposed method outperforms state-of-the-art sampling strategies for dense rewards w.r.t. convergence and peak performance by 26% on average.

Magnetic materials are crucial components of many technologies that could drive the ecological transition, including electric motors, wind turbine generators and magnetic refrigeration systems. Discovering materials with large magnetic moments is therefore an increasing priority. Here, using state-of-the-art machine learning methods, we scan the Inorganic Crystal Structure Database (ICSD) of hundreds of thousands of existing materials to find those that are ferromagnetic and have large magnetic moments. Crystal graph convolutional neural networks (CGCNN), materials graph network (MEGNet) and random forests are trained on the Materials Project database that contains the results of high-throughput DFT predictions. For random forests, we use a stochastic method to select nearly one hundred relevant descriptors based on chemical composition and crystal structure. This gives results that are comparable to those of neural networks. The comparison between these different machine learning approaches gives an estimate of the errors for our predictions on the ICSD database. Validating our final predictions by comparisons with available experimental data, we found 15 materials that are likely to have large magnetic moments and have not been yet studied experimentally.

Energy management systems (EMS) have classically been implemented based on rule-based control (RBC) and model predictive control (MPC) methods. Recent research are investigating reinforcement learning (RL) as a new promising approach. This paper introduces TreeC, a machine learning method that uses the metaheuristic algorithm covariance matrix adaptation evolution strategy (CMA-ES) to generate an interpretable EMS modeled as a decision tree. This method learns the decision strategy of the EMS based on historical data contrary to RBC and MPC approaches that are typically considered as non adaptive solutions. The decision strategy of the EMS is modeled as a decision tree and is thus interpretable contrary to RL which mainly uses black-box models (e.g. neural networks). The TreeC method is compared to RBC, MPC and RL strategies in two study cases taken from literature: (1) an electric grid case and (2) a household heating case. The results show that TreeC obtains close performances than MPC with perfect forecast in both cases and obtains similar performances to RL in the electrical grid case and outperforms RL in the household heating case. TreeC demonstrates a performant application of machine learning for energy management systems that is also fully interpretable.

We present LTC-SE, an improved version of the Liquid Time-Constant (LTC) neural network algorithm originally proposed by Hasani et al. in 2021. This algorithm unifies the Leaky-Integrate-and-Fire (LIF) spiking neural network model with Continuous-Time Recurrent Neural Networks (CTRNNs), Neural Ordinary Differential Equations (NODEs), and bespoke Gated Recurrent Units (GRUs). The enhancements in LTC-SE focus on augmenting flexibility, compatibility, and code organization, targeting the unique constraints of embedded systems with limited computational resources and strict performance requirements. The updated code serves as a consolidated class library compatible with TensorFlow 2.x, offering comprehensive configuration options for LTCCell, CTRNN, NODE, and CTGRU classes. We evaluate LTC-SE against its predecessors, showcasing the advantages of our optimizations in user experience, Keras function compatibility, and code clarity. These refinements expand the applicability of liquid neural networks in diverse machine learning tasks, such as robotics, causality analysis, and time-series prediction, and build on the foundational work of Hasani et al.

In this paper, we present a dynamically reconfigurable hardware accelerator called FADES (Fused Architecture for DEnse and Sparse matrices). The FADES design offers multiple configuration options that trade off parallelism and complexity using a dataflow model to create four stages that read, compute, scale and write results. FADES is mapped to the programmable logic (PL) and integrated with the TensorFlow Lite inference engine running on the processing system (PS) of a heterogeneous SoC device. The accelerator is used to compute the tensor operations, while the dynamically reconfigurable approach can be used to switch precision between int8 and float modes. This dynamic reconfiguration enables better performance by allowing more cores to be mapped to the resource-constrained device and lower power consumption compared with supporting both arithmetic precisions simultaneously. We compare the proposed hardware with a high-performance systolic architecture for dense matrices obtaining 25% better performance in dense mode with half the DSP blocks in the same technology. In sparse mode, we show that the core can outperform dense mode even at low sparsity levels, and a single-core achieves up to 20x acceleration over the software-optimized NEON RUY library.

The operation of electricity grids has become increasingly complex due to the current upheaval and the increase in renewable energy production. As a consequence, active grid management is reaching its limits with conventional approaches. In the context of the Learning to Run a Power Network challenge, it has been shown that Reinforcement Learning (RL) is an efficient and reliable approach with considerable potential for automatic grid operation. In this article, we analyse the submitted agent from Binbinchen and provide novel strategies to improve the agent, both for the RL and the rule-based approach. The main improvement is a N-1 strategy, where we consider topology actions that keep the grid stable, even if one line is disconnected. More, we also propose a topology reversion to the original grid, which proved to be beneficial. The improvements are tested against reference approaches on the challenge test sets and are able to increase the performance of the rule-based agent by 27%. In direct comparison between rule-based and RL agent we find similar performance. However, the RL agent has a clear computational advantage. We also analyse the behaviour in an exemplary case in more detail to provide additional insights. Here, we observe that through the N-1 strategy, the actions of the agents become more diversified.

Consumer's privacy is a main concern in Smart Grids (SGs) due to the sensitivity of energy data, particularly when used to train machine learning models for different services. These data-driven models often require huge amounts of data to achieve acceptable performance leading in most cases to risks of privacy leakage. By pushing the training to the edge, Federated Learning (FL) offers a good compromise between privacy preservation and the predictive performance of these models. The current paper presents an overview of FL applications in SGs while discussing their advantages and drawbacks, mainly in load forecasting, electric vehicles, fault diagnoses, load disaggregation and renewable energies. In addition, an analysis of main design trends and possible taxonomies is provided considering data partitioning, the communication topology, and security mechanisms. Towards the end, an overview of main challenges facing this technology and potential future directions is presented.

We develop a novel graph-based trainable framework to maximize the weighted sum energy efficiency (WSEE) for power allocation in wireless communication networks. To address the non-convex nature of the problem, the proposed method consists of modular structures inspired by a classical iterative suboptimal approach and enhanced with learnable components. More precisely, we propose a deep unfolding of the successive concave approximation (SCA) method. In our unfolded SCA (USCA) framework, the originally preset parameters are now learnable via graph convolutional neural networks (GCNs) that directly exploit multi-user channel state information as the underlying graph adjacency matrix. We show the permutation equivariance of the proposed architecture, which is a desirable property for models applied to wireless network data. The USCA framework is trained through a stochastic gradient descent approach using a progressive training strategy. The unsupervised loss is carefully devised to feature the monotonic property of the objective under maximum power constraints. Comprehensive numerical results demonstrate its generalizability across different network topologies of varying size, density, and channel distribution. Thorough comparisons illustrate the improved performance and robustness of USCA over state-of-the-art benchmarks.

We present a novel approach to efficiently compute tight non-convex enclosures of the image through neural networks with ReLU, sigmoid, or hyperbolic tangent activation functions. In particular, we abstract the input-output relation of each neuron by a polynomial approximation, which is evaluated in a set-based manner using polynomial zonotopes. While our approach can also can be beneficial for open-loop neural network verification, our main application is reachability analysis of neural network controlled systems, where polynomial zonotopes are able to capture the non-convexity caused by the neural network as well as the system dynamics. This results in a superior performance compared to other methods, as we demonstrate on various benchmarks. Keywords: Neural network verification neural network controlled systems reachability analysis polynomial zonotopes formal verification.