In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design parameters) and solvers are required to perform rapid execution. In this study, we suggest a path that potentially opens up a possibility for physics-informed neural networks (PINNs), emerging deep-learning-based solvers, to be considered as one such solver. Although PINNs have pioneered a proper integration of deep-learning and scientific computing, they require repetitive time-consuming training of neural networks, which is not suitable for many-query scenarios. To address this issue, we propose a lightweight low-rank PINNs containing only hundreds of model parameters and an associated hypernetwork-based meta-learning algorithm, which allows efficient approximation of solutions of PDEs for varying ranges of PDE input parameters. Moreover, we show that the proposed method is effective in overcoming a challenging issue, known as failure modes of PINNs.

Accurate short-term electricity price forecasting is crucial for strategically scheduling demand and generation bids in day-ahead markets. While data-driven techniques have shown considerable prowess in achieving high forecast accuracy in recent years, they rely heavily on the quality of input covariates. In this paper, we investigate whether asynchronously published prices as a result of differing gate closure times (GCTs) in some bidding zones can improve forecasting accuracy in other markets with later GCTs. Using a state-of-the-art ensemble of models, we show significant improvements of 22% and 9% in forecast accuracy in the Belgian (BE) and Swedish bidding zones (SE3) respectively, when including price data from interconnected markets with earlier GCT (Germany-Luxembourg, Austria, and Switzerland). This improvement holds for both general as well as extreme market conditions. Our analysis also yields further important insights: frequent model recalibration is necessary for maximum accuracy but comes at substantial additional computational costs, and using data from more markets does not always lead to better performance - a fact we delve deeper into with interpretability analysis of the forecast models. Overall, these findings provide valuable guidance for market participants and decision-makers aiming to optimize bidding strategies within increasingly interconnected and volatile European energy markets.

Numerical simulations have revolutionized the industrial design process by reducing prototyping costs, design iterations, and enabling product engineers to explore the design space more efficiently. However, the growing scale of simulations demands substantial expert knowledge, computational resources, and time. A key challenge is identifying input parameters that yield optimal results, as iterative simulations are costly and can have a large environmental impact. This paper presents an AI-assisted workflow that reduces expert involvement in parameter optimization through the use of Bayesian optimization. Furthermore, we present an active learning variant of the approach, assisting the expert if desired. A deep learning model provides an initial parameter estimate, from which the optimization cycle iteratively refines the design until a termination condition (e.g., energy budget or iteration limit) is met. We demonstrate our approach, based on a sheet metal forming process, and show how it enables us to accelerate the exploration of the design space while reducing the need for expert involvement.

Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep NN models to solve mp-QP with linear constraints, which also exhibit piecewise affine behaviour. However, traditional deep NN applications to mp-QP fall short of providing optimal and feasible predictions, even when trained on large datasets. This study proposes a partially-supervised NN (PSNN) architecture that directly represents the mathematical structure of the global solution function. In contrast to generic NN training approaches, the proposed PSNN method derives a large proportion of model weights directly from the mathematical properties of the optimization problem, producing more accurate solutions despite significantly smaller training data sets. Many energy management problems are formulated as QP, so we apply the proposed approach to energy systems (specifically DC optimal power flow) to demonstrate proof of concept. Model performance in terms of solution accuracy and speed of predictions was compared against a commercial solver and a generic Deep NN model based on classical training. Results show KKT sufficient conditions for PSNN consistently outperform generic NN architectures with classical training using far less data, including when tested on extreme, out-of-training distribution test data. Given its speed advantages over traditional solvers, the PSNN model can quickly produce optimal and feasible solutions within a second for millions of input parameters sampled from a distribution of stochastic demands and renewable generator dispatches, which can be used for simulations and long term planning.

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate optimization solver amounts to estimating a global solution function that maps varying problem input parameters to the corresponding optimal solutions. Work in multiparametric programming (mp) has shown that solutions to quadratic programs (QP) are piece-wise linear functions of the parameters, and researchers have suggested leveraging this property to model mp-QP using NN with ReLU activation functions, which also exhibit piecewise linear behaviour. This paper proposes a NN modeling approach and learning algorithm that discovers the exact closed-form solution to QP with linear constraints, by analytically deriving NN model parameters directly from the problem coefficients without training. Whereas generic DNN cannot guarantee accuracy outside the training distribution, the closed-form NN model produces exact solutions for every discovered critical region of the solution function. To evaluate the closed-form NN model, it was applied to DC optimal power flow problems in electricity management. In terms of Karush-Kuhn-Tucker (KKT) optimality and feasibility of solutions, it outperformed a classically trained DNN and was competitive with, or outperformed, a commercial analytic solver (Gurobi) at far less computational cost. For a long-range energy planning problem, it was able to produce optimal and feasible solutions for millions of input parameters within seconds.

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.

Abstract--In advanced nodes, optimization of power, performance and area (PPA) has become highly complex and challenging. Machine learning (ML) and design-technology co-optimization (DTCO) provide promising mitigations, but face limitations due to a lack of diverse training data as well as long design flow turnaround times (T A T). We propose ArtNet, a novel artificial netlist generator designed to tackle these issues. By producing realistic artificial datasets that more closely match given target parameters, ArtNet enables more efficient PPA optimization and exploration of flows and design enablements. In the context of CNN-based DRV prediction, ArtNet's data augmentation improves F1 score by 0.16 compared to using only the original (real) dataset. In the DTCO context, ArtNet-generated mini-brains achieve a PPA match up to 97.94%, demonstrating close alignment with design metrics of targeted full-scale block designs. S modern designs increase in complexity and scale, improvement of power, performance, and area (PP A) has become more challenging. Place-and-route (P&R) tools rely heavily on heuristics, but struggle with problem scale and the need to balance turnaround time (T A T) against quality of results (QoR). Machine learning (ML) offers the promise of T A T reduction through prediction and optimization of design processes to avoid iterative design loops [24]. However, data requirements of ML are difficult to satisfy, and obtaining high-quality, sharable design datasets remains a key challenge. Restrictions on sharing of proprietary designs and EDA tool outputs hinder creation of comprehensive datasets, limiting the effectiveness of ML models and underlying research efforts. At the same time, the slowdown of Moore's Law has made design-technology co-optimization (DTCO) essential to PP A improvement in advanced nodes [4] [5]. However, co-exploration of the broad solution space for design and technology is gated by large tool and flow T A T on real designs.

We study k -median clustering under the sequential no-substitution setting.

Recent advancements in Large Language Models (LLMs) has lead to the development of agents capable of complex reasoning and interaction with external tools. In enterprise contexts, the effective use of such tools that are often enabled by application programming interfaces (APIs), is hindered by poor documentation, complex input or output schema, and large number of operations. These challenges make tool selection difficult and reduce the accuracy of payload formation by up to 25%. We propose ACE, an automated tool creation and enrichment framework that transforms enterprise APIs into LLM-compatible tools. ACE, (i) generates enriched tool specifications with parameter descriptions and examples to improve selection and invocation accuracy, and (ii) incorporates a dynamic shortlisting mechanism that filters relevant tools at runtime, reducing prompt complexity while maintaining scalability. We validate our framework on both proprietary and open-source APIs and demonstrate its integration with agentic frameworks. To the best of our knowledge, ACE is the first end-to-end framework that automates the creation, enrichment, and dynamic selection of enterprise API tools for LLM agents.