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Baptiste Schubnel

Publications and source records attributed to Baptiste Schubnel.

16 recordsLinked to original sources
arXiv2025

SolarCrossFormer: Improving day-ahead Solar Irradiance Forecasting by Integrating Satellite Imagery and Ground Sensors

Accurate day-ahead forecasts of solar irradiance are required for the large-scale integration of solar photovoltaic (PV) systems into the power grid. However, current forecasting solutions lack the temporal and spatial resolution required by system operators. In this paper, we introduce SolarCrossFormer, a novel deep learning model for day-ahead irradiance forecasting, that combines satellite images and time series from a ground-based network of meteorological stations. SolarCrossFormer uses novel graph neural networks to exploit the inter- and intra-modal correlations of the input data and improve the accuracy and resolution of the forecasts. It generates probabilistic forecasts for any location in Switzerland with a 15-minute resolution for horizons up to 24 hours ahead. One of the key advantages of SolarCrossFormer its robustness in real life operations. It can incorporate new time-series data without retraining the model and, additionally, it can produce forecasts for locations without input data by using only their coordinates. Experimental results over a dataset of one year and 127 locations across Switzerland show that SolarCrossFormer yield a normalized mean absolute error of 6.1 % over the forecasting horizon. The results are competitive with those achieved by a commercial numerical weather prediction service.

cs.LG↗
arXiv2024

Risk-aware Scheduling and Dispatch of Flexibility Events in Buildings

Residential and commercial buildings, equipped with systems such as heat pumps (HPs), hot water tanks, or stationary energy storage, have a large potential to offer their consumption flexibility as grid services. In this work, we leverage this flexibility to react to consumption requests related to maximizing self-consumption and reducing peak loads. We employ a data-driven virtual storage modeling approach for flexibility prediction in the form of flexibility envelopes for individual buildings. The risk-awareness of this prediction is inherited by the proposed scheduling algorithm. A Mixed-integer Linear Program (MILP) is formulated to schedule the activation of a pool of buildings in order to best respond to an external aggregated consumption request. This aggregated request is then dispatched to the active individual buildings, based on the previously determined schedule. The effectiveness of the approach is demonstrated by coordinating up to 500 simulated buildings using the Energym Python library and observing about 1.5 times peak power reduction in comparison with a baseline approach while maintaining comfort more robustly. We demonstrate the scalability of the approach by solving problems with 2000 buildings in about 21 seconds, with solving times being approximately linear in the number of considered assets.

eess.SY↗
arXiv2022

Uncertainty-aware Flexibility Envelope Prediction in Buildings with Controller-agnostic Battery Models

Buildings are a promising source of flexibility for the application of demand response. In this work, we introduce a novel battery model formulation to capture the state evolution of a single building. Being fully data-driven, the battery model identification requires one dataset from a period of nominal controller operation, and one from a period with flexibility requests, without making any assumptions on the underlying controller structure. We consider parameter uncertainty in the model formulation and show how to use risk measures to encode risk preferences of the user in robust uncertainty sets. Finally, we demonstrate the uncertainty-aware prediction of flexibility envelopes for a building simulation model from the Python library Energym.

eess.SY↗
arXiv2021

Spatio-temporal graph neural networks for multi-site PV power forecasting

Accurate forecasting of solar power generation with fine temporal and spatial resolution is vital for the operation of the power grid. However, state-of-the-art approaches that combine machine learning with numerical weather predictions (NWP) have coarse resolution. In this paper, we take a graph signal processing perspective and model multi-site photovoltaic (PV) production time series as signals on a graph to capture their spatio-temporal dependencies and achieve higher spatial and temporal resolution forecasts. We present two novel graph neural network models for deterministic multi-site PV forecasting dubbed the graph-convolutional long short term memory (GCLSTM) and the graph-convolutional transformer (GCTrafo) models. These methods rely solely on production data and exploit the intuition that PV systems provide a dense network of virtual weather stations. The proposed methods were evaluated in two data sets for an entire year: 1) production data from 304 real PV systems, and 2) simulated production of 1000 PV systems, both distributed over Switzerland. The proposed models outperform state-of-the-art multi-site forecasting methods for prediction horizons of six hours ahead. Furthermore, the proposed models outperform state-of-the-art single-site methods with NWP as inputs on horizons up to four hours ahead.

cs.LG↗
arXiv2020

State space models for building control: how deep should you go?

Power consumption in buildings show non-linear behaviors that linear models cannot capture whereas recurrent neural networks (RNNs) can. This ability makes RNNs attractive alternatives for the model-predictive control (MPC) of buildings. However RNN models lack mathematical regularity which makes their use challenging in optimization problems. This work therefore systematically investigates whether using RNNs for building control provides net gains in an MPC framework. It compares the representation power and control performance of two architectures: a fully non-linear RNN architecture and a linear state-space model with non-linear regressor. The comparison covers five instances of each architecture over two months of simulated operation in identical conditions. The error on the one-hour forecast of temperature is 69% lower with the RNN model than with the linear one. In control the linear state-space model outperforms by 10% on the objective function, shows 2.8 times higher average temperature violations, and needs a third of the computation time the RNN model requires. This work therefore demonstrates that in their current form RNNs do improve accuracy but on balance well-designed linear state-space models with non-linear regressors are best in most cases of MPC.

eess.SY↗
arXiv2020

A hybrid learning method for system identification and optimal control

We present a three-step method to perform system identification and optimal control of non-linear systems. Our approach is mainly data driven and does not require active excitation of the system to perform system identification. In particular, it is designed for systems for which only historical data under closed-loop control are available and where historical control commands exhibit low variability. In a first step, simple simulation models of the system are built and run under various conditions. In a second step, a neural network architecture is extensively trained on the simulation outputs to learn the system physics, and retrained with historical data from the real system with stopping rules. These constraints avoid overfitting that arise by fitting closed-loop controlled systems. By doing so, we obtain one (or many) system model(s), represented by this architecture, and whose behaviour can be chosen to match more or less the real system. Finally, state-of-the-art reinforcement learning with a variant of domain randomization and distributed learning is used for optimal control of the system. We first illustrate the model identification strategy with a simple example, the pendulum with external torque. We then apply our method to model and optimize the control of a large building facility located in Switzerland. Simulation results demonstrate that this approach generates stable functional controllers which outperform on comfort and energy benchmark rule-based controllers.

eess.SY↗
arXiv2016

A "Garden of Forking Paths" - the Quantum Mechanics of Histories of Events

We present a short survey of a novel approach, called "ETH approach", to the quantum theory of events happening in isolated physical systems and to the effective time evolution of states of systems featuring events. In particular, we attempt to present a clear explanation of what is meant by an "event" in quantum mechanics and of the significance of this notion. We then outline a theory of direct (projective) and indirect observations or recordings of physical quantities and events. Some key ideas underlying our general theory are illustrated by studying a simple quantum-mechanical model of a mesoscopic system.

quant-ph↗
arXiv2016

Scattering theory for Lindblad master equations

We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space.

math-ph↗
arXiv2015

Spectral Analysis of a Model for Quantum Friction

An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude which is typically proportional to a power of its speed. We study here the quantum equivalent of a classical Hamiltonian model for this friction phenomenon that was proposed in [11]. More precisely, we study the spectral properties of the quantum Hamiltonian and compare the quantum and classical situations. Under suitable conditions on the infrared behaviour of the model, we prove that the Hamiltonian at fixed total momentum has no ground state except when the total momentum vanishes, and that its spectrum is otherwise absolutely continuous.

math-ph↗
arXiv2015

Indirect retrieval of information and the emergence of facts in quantum mechanics

Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition measurements in quantum mechanics. Our attempt leads us to make novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.

math-ph↗
arXiv2015

On the probabilistic nature of quantum mechanics and the notion of closed systems

The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the interaction between $P$ and $Q$, we show that the system $P$ behaves as a closed system if the initial state of $P \vee Q$ belongs to a large class of states, including ones exhibiting entanglement between $P$ and $Q$. We use our results to illustrate the non-deterministic nature of quantum mechanics. Studying a specific example, we show that assigning an initial state and a unitary time evolution to a quantum system is generally not sufficient to predict the results of a measurement with certainty.

math-ph↗
arXiv2015

Quantum Electrodynamics of Atomic Resonances

A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass $m$, finitely many excited states and an electric dipole moment, $\vec{d}_0 = -λ_{0} \vec{d}$, where $\| d^{i}\| = 1,$ $ i=1,2,3,$ and $λ_0$ is proportional to the elementary electric charge. The interaction of the atom with the radiation field is described with the help of the Ritz Hamiltonian, $-\vec{d}_0\cdot \vec{E}$, where $\vec{E}$ is the electric field, cut off at large frequencies. A mathematical study of the Lamb shift, the decay channels and the life times of the excited states of the atom is presented. It is rigorously proven that these quantities are analytic functions of the momentum $\vec{p}$ of the atom and of the coupling constant $λ_0$, provided $|\vec{p}| < mc$ and $| \Im\vec{p} |$ and $| λ_{0} |$ are sufficiently small. The proof relies on a somewhat novel inductive construction involving a sequence of `smooth Feshbach-Schur maps' applied to a complex dilatation of the original Hamiltonian, which yields an algorithm for the calculation of resonance energies that converges super-exponentially fast.

math-ph↗
arXiv2014

The preparation of states in quantum mechanics

The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.

math-ph↗
arXiv2012

Dimensional Reduction without Extra Continuous Dimensions

We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and generalized connections associated with the "geometry" of space-times with discrete extra dimensions. We apply our formalism to theories of gauge- and gravitational fields and find natural geometrical origins for an axion- and a dilaton field, as well as a Higgs field.

math-ph↗
arXiv2012

Do We Understand Quantum Mechanics - Finally?

After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator algebras. We then review some basic aspects of quantum mechanics and, in particular, of its interpretation. We attempt to clarify what Quantum Mechanics tells us about Nature when appropriate experiments are made. We discuss the importance of the mechanisms of "dephasing" and "decoherence" in associating "facts" with possible events and rendering complementary possible events mutually exclusive.

quant-ph↗