Giovanni B. Esposito

Hiari Pizzini Cavagna, Andrea Proia, Giacomo Madella et al.

Large Language Models (LLMs) inference is central to modern AI applications, dominating worldwide datacenter workloads, making it critical to predict its energy footprint. Existing approaches estimate energy consumption as a simple linear function of input and output sequence. However, by analyzing the autoregressive structure of Transformers, which implies a fundamentally non-linear relationship between input and output sequence lengths and energy consumption, we demonstrate the existence of a generation energy minima. Peak efficiency occurs with short-to-moderate inputs and medium-length outputs, while efficiency drops sharply for long inputs or very short outputs. Consequently, we propose SweetSpot, an analytical model derived from the computational and memory-access complexity of the Transformer architecture, which accurately characterizes the efficiency curve as a function of input and output lengths. To assess accuracy, we measure energy consumption using TensorRT-LLM on NVIDIA H100 GPUs across a diverse set of LLMs ranging from 1B to 9B parameters, including OPT, LLaMA, Gemma, Falcon, Qwen2, and Granite. We test input and output lengths from 64 to 4096 tokens and achieve a mean MAPE of 1.79%. Our results show that aligning sequence lengths with these efficiency "sweet spots" reduce energy usage, up to 33.41x, enabling informed truncation, summarization, and adaptive generation strategies in production systems.

Sebastiano Mengozzi, Giovanni B. Esposito, Michelangelo Bin et al.

This work addresses the full-information output regulation problem for nonlinear systems, assuming the states of both the plant and the exosystem are known. In this setting, perfect tracking or rejection is achieved by constructing a zero-regulation-error manifold $π(w)$ and a feedforward input $c(w)$ that render such manifold invariant. The pair $(π(w), c(w))$ is characterized by the regulator equations, i.e., a system of PDEs with an algebraic constraint. We focus on accurately solving the regulator equations introducing a physics-informed neural network (PINN) approach that directly approximates $π(w)$ and $c(w)$ by minimizing the residuals under boundary and feasibility conditions, without requiring precomputed trajectories or labeled data. The learned operator maps exosystem states to steady state plant states and inputs, enables real-time inference and, critically, generalizes across families of the exosystem with varying initial conditions and parameters. The framework is validated on a regulation task that synchronizes a helicopter's vertical dynamics with a harmonically oscillating platform. The resulting PINN-based solver reconstructs the zero-error manifold with high fidelity and sustains regulation performance under exosystem variations, highlighting the potential of learning-enabled solvers for nonlinear output regulation. The proposed approach is broadly applicable to nonlinear systems that admit a solution to the output regulation problem.