Symbolic regression is a set of methods designed to discover symbolic, human-readable formulas that best fit a given dataset. It is a powerful tool for model discovery, enabling the identification of underlying patterns or dynamics in an unknown system. Modern symbolic regression methods are highly applicable to fundamental science. The outcomes of symbolic regression methods are the models can take the form of algebraic expressions as well as differential equations. However, non-linear symbolic regression methods often face significant challenges, including convergence to local minima and enforcing the sparsity in the resulting expression coefficients. Addressing these issues is crucial to improving the interpretability and robustness of the derived models. In this project, the student will have the opportunity to work on enhancing optimization strategies for previously proposed non-linear symbolic regression methods. This project could serve as an excellent entry point into the fields of symbolic regression and model discovery, with broad applications in advancing fundamental scientific understanding.

[1] Makke, N., & Chawla, S. (2024). Interpretable scientific discovery with symbolic regression: a review. Artificial Intelligence Review, 57(1), 2.

[2] Sahoo, S., Lampert, C., & Martius, G. (2018, July). Learning equations for extrapolation and control. In International Conference on Machine Learning (pp. 4442-4450). Pmlr.

You can apply by directly contacting Sergei Garmaev.

Description
This project explores graph neural network (GNN) models as efficient surrogates for incompressible fluid flow simulations. Using shear flow data from Polymathic AI, students will implement and benchmark GNS/MeshGraphNet, E(3)-GNN, and GMN architectures. The goal is to evaluate long-range rollout performance and generalization to new initial and boundary conditions.

Requirements
Python programming, machine learning knowledge, and familiarity with GNNs or CFD are recommended.

Keywords: Graph neural networks, Physics prior, Fluid mechanics

You can apply via SiROP or directly contact Vinay Sharma.

Reconstructing time-varying graph signals is a critical challenge in graph machine learning and graph signal processing, with various applications such as missing data imputation in sensor networks and time-series forecasting. Effectively addressing these tasks requires accurately capturing the spatio-temporal information inherent in these graph signals. Current methods, however, often rely exclusively on either graph signal processing methods or graph neural networks, limiting their ability to fully leverage the strengths of both approaches. This project aims to develop a new model for time-varying graph signal reconstruction, integrating the inductive bias from graph signal processing to graph neural networks.

Requirements:
1. Experience in Python and PyTorch
2. Familiar with graph machine learning and/or graph signal processing.

Keywords: Graph neural networks, graph signal processing, time-series reconstruction.

You can apply via SiROP or directly contact Zepeng Zhang.

• Conduct a comprehensive literature review about building energy modeling techniques and hybrid models
• Analyze available large-scale building energy data
• Explore hybrid models for time series regression
• Evaluate proposed methodologies and compare it to a variety of benchmark models.

Degradation analysis and prediction are crucial for maintaining the reliability and efficiency of industrial systems. Still, real systems are often affected by external factors – such as noise, measurement error, and diverse operating conditions – which may hide signs of true degradation. It is therefore critical to be able to differentiate superficial dynamical fluctuations from essential, potentially catastrophic changes in behavior.

We aim to tackle this problem through the lens of topology. The topological theory of structural stability allows us to give a precise description of a system’s fundamental qualitative behavior, allowing us to represent failure and faults as sudden topological shifts, or bifurcations. Still, to extract a true topological description from data remains a major challenge.

Our objective for this project is to leverage recent advances in machine learning to obtain dynamic, data-driven topological descriptions of real dynamical systems by combining Neural Differential Equations and the paradigm of topological conjugation. We will then analyse what information may be extracted from real systems changing topology and how this may be used to identify faulty systems.

Pre-requisites:
Prospective candidates are expected to possess a foundational understanding of machine learning and ordinary differential equations, as well as experience programming in Python or Julia. Knowledge on topology or dynamical systems theory is a plus, but not required. To apply, contact Arthur Bizzi directly.

Time-series data is increasingly prevalent across various domains, including finance, healthcare, and environmental monitoring. The ability to extract meaningful information from time-series data is crucial for prediction, classification, and anomaly detection. This project focuses on exploring different time-series representations and their impact on machine-learning tasks.

Objectives

1. Benchmarking Time-Series Representations: Investigate the performance of various time-series representations including Fast Fourier Transform (FFT), Recurrence Plot (RP), Gramian Angular Field (GAF), and Markov Transition Field (MTF) in the context of machine learning tasks.

2. Design of Fusion Method: Develop a novel method to fuse information from these representations, aiming to leverage their combined strengths.

3. Evaluation on Diverse Datasets: Assess the effectiveness of the proposed method on a variety of datasets pertaining to Time-Series Classification, Forecasting, and Anomaly Detection.

Methodology

1. Literature Review: Conduct a comprehensive review of existing literature on time-series representation methods and their applications.

2. Implementation of Representations: Implement and fine-tune FFT, RP, GAF, and MTF, ensuring a fair and consistent basis for comparison.

3. Benchmarking: Evaluate each representation method across multiple datasets, using standard metrics relevant to classification, forecasting, and anomaly detection.

4. Fusion Method Development: Design a fusion algorithm to integrate the different representations, potentially using techniques like feature concatenation, ensemble methods, or deep learning architectures.

5. Experimental Evaluation: Test the fusion method across the same datasets used for benchmarking, comparing its performance against the individual representation methods.

You can apply via SiROP or directly contact Hao Dong.

Denoising Diffusion Probabilistic Models (DDPMs) are a highly popular class of deep generative models that have been successfully applied to various problems, including image and video generation. Recently, there have been attempts to apply these models to time-series data. However, they are not enough for modeling spatial-temporal interactions. They primarily focus on temporal dependencies within individual sensors, neglecting the spatial correlations between different nodes. In reality, objects are spatially correlated with each other. This project aims to explore a graph-based denoising diffusion probabilistic model to jointly capture both temporal dependencies and spatial interactions.

Recent advances in neural scene reconstruction, such as Neural Radiance Fields (NeRF) and Gaussian Splatting, have significantly improved the performance of downstream tasks, including novel view synthesis and geometric reconstruction. Building on these innovations, multi-modal approaches have been explored to incorporate additional scene attributes such as depth, surface normals, thermal data, and semantic information to enrich existing scene representations. However, current multi-modal methods often rely on a tightly coupled correspondence between RGB data and other modalities, which limits their applicability in uncontrolled, real-world scenarios.

Description:
This project aims to address the challenge of strong cross-modal dependencies in 3D reconstruction, with a particular focus on RGB and thermal imaging. The goal is to develop robust techniques that can establish correspondences between different modalities, or align image features in three-dimensional space, thereby enabling accurate reconstruction without the need for strict pixel-level alignment across modalities.

Objectives:
 – Conduct a comprehensive literature review on multi-modal 3D reconstruction techniques, with an emphasis on robustness and cross-modal integration
 – Investigate contrastive learning approaches for identifying correspondences between RGB and non-RGB modalities
 – Explore strategies for 3D-space feature alignment and rendering-based pose optimization
 – Extend the reconstruction framework to incorporate additional modalities, including semantic labels and inputs with weak or no geometric correlation

Keywords: Multi-modal fusion, Visual-based 3D reconstruction, thermal imaging

You can apply by directly contacting Chenghao Xu.

• Conduct a comprehensive literature review about Computer Vision techniques for building parameter extraction
• Investigate suitable settings to train the Computer Vision model in the context of Urban Building Energy Modeling on a large scale
• Explore the proposed methodology in the case of Swiss Lidar data on municipality or city-level

In this project, you will focus on the task of learning/simulating rigid objects dynamics from videos, with the end-goal of predicting future or alternative trajectories for the objects in the scene. This task includes the decomposition of a visual scene into multiple blocks (identifying individual objects), the modeling of their evolution and interactions in the scene (positions, velocities, collisions, …), and the prediction of future (or alternative) trajectories (also called rollout).

Keywords: Computer Vision, Mechanics, Scene Understanding, Object-centric Learning

You can apply via IS-Academia – project #14165 or directly contact Amaury Wei.

Most deep models are trained under a close-world assumption and hence do not possess knowledge of what they do not know, leading to over-confident and inaccurate predictions for unknown objects. Out-of-distribution (OOD) detection, which aims to identify unknown objects, has attracted much attention as it plays a vital role in a variety of applications such as industrial inspection, medical diagnosis, and autonomous driving. One of the primary challenges of effective OOD lies in the wide-existing domain shift in the real world. The testing dataset might have a significant distribution from the training data of deep learning models. Thus, it is even more difficult for the model to distinguish between the domain difference and the OOD objects. In this task, the student is expected to work on the OOD detection task with domain shift. Specifically, we focus on test-time domain adaptation, which focuses on OOD detection during inference time online. The potential application case can be found here: https://www.epfl.ch/labs/cvlab/data/road-anomaly/. Overall, the goal of this project is to improve the OOD performance on new domains through the use of test-time domain adaptation techniques. The student is expected to undertake the following tasks in this project: – explore current test-time domain adaptation methods – improve those methods and modify them for OOD detection.

You can apply via SiROP or directly contact Han Sun.