We are the Machine Learning for Physical Science group, located at the Eindhoven University of Technology. Our group develops advanced computational methods combining Scientific Machine Learning, Deep Generative Modeling, and Deep Geometric Learning to accelerate scientific discovery. We focus on building efficient emulators from synthetic and experimental data, incorporating domain knowledge and physical principles to address challenges in materials science, mechanical engineering, fluid dynamics, and nuclear fusion.
We are pushing the boundaries of deep generative modeling to overcome limitations inherent in scientific computing and the simulation of dynamical systems. Our research focuses on building highly efficient and precise emulators by developing Machine Learning models from both synthetic and experimental data. These emulators empower us to design novel materials with targeted chemical and mechanical properties, model complex pedestrian dynamics, and simulate plasmas within nuclear fusion devices, ultimately contributing to advancements in these respective fields.
A key aspect of our approach is the incorporation of domain knowledge. We leverage known symmetries and physical principles to develop data-efficient and scalable models. Furthermore, we are dedicated to establishing robust, validation methodologies to ensure the reliability and trustworthiness of our solutions.
Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances in deep generative modeling and geometric deep learning enable probabilistic simulation by learning complex trajectory distributions while respecting intrinsic permutation and time-shift symmetries. However, trajectories of N-body systems are commonly characterized by high sensitivity to perturbations leading to bifurcations, as well as multi-scale temporal and spatial correlations. To address these challenges, we introduce STFlow (Spatio-Temporal Flow), a generative model based on graph neural networks and hierarchical convolutions. By incorporating data-dependent couplings within the Flow Matching framework, STFlow denoises starting from conditioned random-walks instead of Gaussian noise. This novel informed prior simplifies the learning task by reducing transport cost, increasing training and inference efficiency. We validate our approach on N-body systems, molecular dynamics, and human trajectory forecasting. Across these benchmarks, STFlow achieves the lowest prediction errors with fewer simulation steps and improved scalability.
Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them accurately and quickly, in order to tune their mechanical properties. Since conventional simulations using the finite element method entail a high computational cost, in this article we aim to develop a machine learning-based approach that scales favorably to serve as a surrogate model. To ensure that the model is also able to handle various microstructures, including those not encountered during training, we include the microstructure as part of the network input. Therefore, we introduce a graph neural network that predicts global quantities (energy, stress, stiffness) as well as the pattern transformations that occur (the kinematics) in hyperelastic, two-dimensional, microporous materials. Predicting these pattern transformations means predicting the displacement field. To make our model as accurate and data-efficient as possible, various symmetries are incorporated into the model. The starting point is an 𝐸(𝑛)-equivariant graph neural network (which respects translation, rotation and reflection) that has periodic boundary conditions (i.e., it is in-/equivariant with respect to the choice of RVE), is scale in-/equivariant, can simulate large deformations, and can predict scalars, vectors as well as second and fourth order tensors (specifically energy, stress and stiffness). The incorporation of scale equivariance makes the model equivariant with respect to the similarities group, of which the Euclidean group 𝐸(𝑛) is a subgroup. We show that this network is more accurate and data-efficient than graph neural networks with fewer symmetries. To create an efficient graph representation of the finite element discretization, we use only the internal geometrical hole boundaries from the finite element mesh to achieve a better speed-up and scaling with the mesh size.
Understanding pedestrian crowd dynamics is a fundamental challenge in active matter physics and crucial for efficient urban infrastructure design. Complexity emerges from social interactions, which are often qualitatively modeled as distance-based additive forces. Endeavors towards quantitative characterizations have been limited by a trade-off between parametric control in laboratory studies and statistical resolution of large-scale real-world measurements. To bridge this gap, we propose a virtual surrogate experimentation paradigm that combines laboratory-like control with real-world statistical resolution. Our approach hinges on a generative simulation model based on graph neural networks, which we train on real-world pedestrian tracking data and validate against key statistical properties of crowd dynamics. Our surrogate experiments not only reproduce known experimental results on collision avoidance, but also reveal new insights into N-body interactions in crowds, which have remained poorly understood. We find that these interactions are topological, with individuals reacting to a limited number of neighbors within a narrow field of view. Our study exemplifies how data-driven approaches can uncover fundamental interaction structures in social systems, even when only uncontrolled measurements are available. This approach opens new avenues for scientific discovery in complex systems where laboratory studies are prohibitive, from crowd dynamics and animal behavior to opinion formation.
Highlighted projects
These are some interesting projects we are currently working on. All our projects can be
found
on the Projects page.
Simulating Deformable Interfaces of Rising Bubbles
Bubbly flows appear in many industrial and environmental processes, where the motion,
deformation, and interaction of bubbles strongly influence mixing, transport, and
overall system behavior. These systems are difficult to model because they combine
many-body hydrodynamic interactions with evolving interface geometry over time.
Our work studies learning-based surrogate models for bubbly-flow dynamics using
high-fidelity Front-Tracking simulation data. To support this, we have built a
time-resolved dataset of deformable bubble swarms that includes both centroid
trajectories and compact spherical-harmonic descriptions of bubble shape. On the
modeling side, we are looking at graph neural networks and related spatiotemporal
architectures that can incorporate interaction structure and physical context, with
the broader goal of developing efficient neural simulators for long-horizon prediction
of deformable multiphase flows.
Deformation of bubble interface meshes represented using spherical harmonics
trajectories [1].
Snapshots of bubble swarm data for different diameters and void factions [1].
Data-Coupled Flow Matching
Understanding and simulating complex dynamical systems is a central theme of our research.
Many scientific and societal systems, ranging from interacting particles in physics and
molecular dynamics to groups of humans navigating shared spaces can be described as
geometric
trajectories of multiple interacting entities. These systems are difficult to
model as they exhibit strong coupling between agents, multi-scale temporal structure and
sensitivity to perturbations At the same time, practical simulators benefit from being
probabilistic, capturing uncertainty and multimodality while being computationally efficient
at scale. Our work investigates how modern generative modeling, in particular flow
matching-based methods, can be adapted to respect the structure of these systems while
avoiding the inefficiencies of autoregressive rollouts and uninformed Gaussian priors.
We are currently researching data-coupled generative priors for
conditional trajectory simulation. Rather than initializing generative models just from
generic Gaussian noise, we construct informed priors that are directly conditioned on
observed
initial
frames, embedding basic dynamical structure such as continuity and inertia. This reduces the
transport cost between prior and target trajectory distributions, simplifies the learned
vector fields, and enables accurate simulation with very few integration steps. This line of
work has demonstrated state-of-the-art accuracy and improved scaling on
benchmarks in N-body physics, molecular dynamics, and human trajectory forecasting. More
broadly, our work is trying to advance a principled view of prior design in conditional
generative modeling for dynamical systems, aiming to build scalable, symmetry-aware
simulators
that generalize across domains and temporal horizons.
Denoising animation from predictions of STFlow on an N-Body gravitational system
Model architecture of Spatio-Temporal Flow (paper),
describing a permutation-equivariant and convolution-based flow matching model
