Julia Sohkanen

Julia Sohkanen (Sanders)

I am a university-funded doctoral student at the University of Helsinki in Finland.

statistical physics, machine learning

email: firstname.sanders@helsinki.fi

Department of Mathematics and Statistics
University of Helsinki

Finland

Publications

Optimal Control of Underdamped Systems: An Analytic Approach
Julia Sanders, Marco Baldovin, Paolo Muratore-Ginanneschi

Motivated by the design of nanoscale electronic components, we find protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized in the underdamped dynamics.

J Stat Phys 191, 117 (2024).

Minimal work protocols for inertial particles in non-harmonic traps
Julia Sanders, Marco Baldovin, Paolo Muratore-Ginanneschi

We approximate the solution of an optimal control problem minimizing mean entropy production in the underdamped dynamics, modelling Landauer's principle at nanoscale.

Phys. Rev. E 111, 034127 (2025).

On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
Julia Sanders, Paolo Muratore-Ginanneschi

A study of Monte Carlo methods that can be used in the numerical integration of PDEs arising in optimal control problems. In particular, we demonstrate the methods with a prototype algorithm for solving a Schrodinger bridge using machine learning. We parametrise the drift by a feed forward neural network and use stationarity conditions of the first order optimality equations to perform a gradient descent.
Optimal Control of Engineered Swift Equilibration of Nanomechanical Oscillators
Julia Sanders, Paolo Muratore-Ginanneschi

We propose a reformulation of the problem of optimally controlled transitions in stochastic thermodynamics. We impose that any terminal cost specified by a thermodynamic functional should depend only on state variables and not on control protocols, according to the canonical Bolza form. In this way, we can unambiguously discriminate between transitions at minimum dissipation between genuine equilibrium states, and transitions at minimum work driving a system from a genuine equilibrium to a non-equilibrium state.

Masters Thesis

Talks and Seminars

A Short Introduction to Proximal Operators Mathematical Perspective on Machine Learning, University of Helsinki.
Proximal operators are used frequently in optimisation because they generalise well to high dimensional problems and work with non-smooth functions. During the seminar, I will introduce the proximal operator and give an overview of its basic properties. I will also give some examples of proximal algorithms for minimisation. Finally, I will illustrate a proximal algorithm (Caluya & Halder 2020) to find a numerical approximation of a solution to Fokker-Planck PDE equation.

A Short Introduction to Diffusion models Domast Students' Seminar, University of Helsinki.
Diffusion models are used for image generation: if we add noise to an image we get noise, but, when reversed, we can use this process to generate new images. In the talk, I will give an overview of how these types of models work, and in particular take a more detailed look at the theory behind score based generative models.

A Numerical Approach to Optimal Control of Underdamped Systems La Sapienza, University of Rome, Italy.
A look at the numerical methods used in computing estimates in the multiscale perturbative theory and some machine learning techniques that can be applied to the problem.

Conference Visits

Scientific Advisory Board Invited Oral Presentation, "First" Center of Excellence of the Academy of Finland, University of Helsinki

Workshop on Optimal Transport, Berlin, Germany.
Poster Presentation Optimal Control of Underdamped Systems: A Numeric Approach

STATPHYS 29, Florence, Italy
Oral Presentation "Optimal Control of Underdamped Systems"

AI DAY, Aalto University, Helsinki
Modelling Nanoscale Bit Erasure with Neural Networks