PhD-student: Physical Learning in Dynamical Systems

AMOLF; Amsterdam; On-site; EUR 32,000 - 38,000; Full time

Benefits offered by this job

Housing assistance

Visa support

Transport costs covered

Furnishing expenses

Job summary

AMOLF, located at Amsterdam Science Park, seeks a motivated PhD student to study the theory of learning in dynamical physical systems within the Learning Machines group. The ERC Starting Grant project aims to develop a physics-based framework for learning in adaptive matter under time-dependent dynamics.

You will contribute to developing local learning rules, compare to gradient-based methods, and explore the boundaries of learning in non-equilibrium systems, with access to large-scale

Qualifications

• PhD candidates must meet MSc degree requirements.
• Good verbal and written English communication skills required.
• Experience with coding (Python/Matlab) and numerical methods.

Responsibilities

• Develop local learning rules for dynamical physical systems.
• Compare physical learning approaches to gradient-based methods.
• Investigate when and why physical learning succeeds or fails.
• Explore the role of feedback, non-equilibrium dynamics, and task complexity in learning.
• Develop efficient simulation tools for adaptive dynamical networks.
• Identify scaling laws, phase boundaries, and universal features of learning in matter.

Skills

Coding

Numerical methods

English communication

Python

MATLAB

Education

MSc degree

Tools

Python

MATLAB

Job description

Work Activities

We are seeking a motivated PhD student to join our learning machines group at AMOLF and work on the theory of learning in dynamical physical systems, as part of an ERC Starting Grant project on Physical Learning in Dynamical Systems (PhyLDS). Learning is often viewed as a computational process that takes place in brains or computers. Yet many physical systems, from biological networks to adaptive materials, continuously modify their behavior based on past experience. Despite the ubiquity of such adaptive phenomena, physics still lacks a general understanding of how learning emerges in dynamical systems that operate far from equilibrium. In this project, we will develop a new theoretical framework for learning in physical systems with time-dependent dynamics. Unlike conventional machine learning algorithms, these systems learn through local interactions and physical feedback, without centralized optimization or backpropagation. We will investigate how learning is constrained by locality, causality, non-reciprocity, and dissipation, and how these constraints shape the ability of matter to learn. The project combines analytical theory with large-scale numerical simulations. We will study diverse classes of adaptive dynamical networks, including flow networks, mechanical networks, and neuronal systems. A central goal is to identify the physical principles that govern learning in these systems, including scaling laws, phase diagrams, and fundamental limits.

The PhD student will contribute to:

• Developing local learning rules for dynamical physical systems;
• Comparing physical learning approaches to idealized gradient-based methods;
• Investigating when and why physical learning succeeds or fails;
• Exploring the role of feedback, non-equilibrium dynamics, and task complexity in learning;
• Developing efficient simulation tools for adaptive dynamical networks;
• Identifying scaling laws, phase boundaries, and universal features of learning in matter.

The project offers a unique opportunity to work at the intersection of condensed matter physics, non-equilibrium statistical mechanics, complex systems, machine learning, and biological physics. The successful candidate will help establish a new physics of adaptive matter and contribute to a growing international research effort aimed at understanding learning as a physical phenomenon.

For more information about our work, see:

• [1] Stern and Murugan, Learning without neurons in physical systems, Ann Rev Cond Matt Phys 14, 417 (2023)
• [2] Stern, Hexner, Rocks and Liu, Supervised learning in physical networks: From machine learning to learning machines, Phys. Rev. X 11, 021045 (2021)
• [3] Stern, Frim, Candás, Liu and Balasubramanian, Contrastive learning in tunable dynamical system, arXiv:2603.26969 (2026)

Qualifications

We seek candidates with a strong background in physics, mechanical engineering, materials science, or computer science with an interest in learning theory, broadly defined, condensed matter and complex systems. Excellent candidates with training in any area of science or engineering will be considered. PhD candidates must meet the requirements for an MSc degree. Good verbal and written communication skills in English are required. Other advantageous qualities include experience with coding (Python\\Matlab) and numerical methods, as well as familiarity with concepts in complex dynamical systems, physical memories or machine learning. We strongly believe in the benefits of an inclusive and diverse research environment, and welcome applicants with any background.

Work environment

AMOLF is a part of NWO-I and initiate and performs leading fundamental research on the physics of complex forms of matter, and to create new functional materials, in partnership with academia and industry. The institute is located at Amsterdam Science Park and currently employs about 140 researchers and 80 support employees.

The Learning Machines group is a new group at AMOLF, led by Menachem (Nachi) Stern, and focuses on the development of fundamental understanding and theories regarding learning, from a physical perspective, under real world constraints.

Our group members work closely together with extensive support from the group leader and AMOLF resources in all aspects of design, realization, and interpretation of computational models of physical learning systems. We have a strong focus on stimulating development of students in all professional aspects, as well as collaborations with other researchers at our institute and beyond. Moreover, we work closely together with international groups and companies.

Working conditions

The working atmosphere at the institute is largely determined by young, enthusiastic, mostly foreign employees. Communication is informal and runs through short lines of communication.

The position is intended as full-time (40 hours / week, 12 months / year) appointment in the service of the Netherlands Foundation of Scientific Research Institutes (NWO-I) for the duration of four years.

The starting salary is 3.115 Euro’s gross per month and a range of employment benefits.

After successful completion of the PhD research a PhD degree will be granted at a Dutch University.

Several courses are offered, specially developed for PhD-students.

AMOLF assists any new foreign PhD-student with housing and visa applications and compensates their transport costs and furnishing expenses.

Application

Online screening may be part of the selection.

For further information about the position, please contact:

Dr. Menachem Stern

E-mail: [e-mail]

Diversity code

AMOLF is highly committed to an inclusive and diverse work environment: we want to develop talent and creativity by bringing together people from different backgrounds and cultures. We recruit and select on the basis of competencies and talents. We strongly encourage anyone with the right qualifications to apply for the vacancy, regardless of age, gender, origin, sexual orientation or physical ability.

AMOLF has won the NNV Diversity Award 2022, which is awarded every two years by the Netherlands Physical Society for demonstrating the most successful implementation of equality, diversity and inclusion (EDI).