document

Learning Interpretable Reduced-order Models for Jumping Quadrupeds

Buriani, Gioele (author)

This work introduces a novel methodology for the development of interpretable reduced-order dynamic models specifically tailored for jumping quadruped robots. Leveraging Symbolic Regression combined with autoencoder neural networks, the framework autonomously derives symbolic equations from data and fundamental physics principles capturing the...

master thesis 2024

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SymFormer: End-to-End Symbolic Regression Using Transformer-Based Architecture

Vastl, Martin (author), Kulhanek, Jonas (author), Kubalik, Jiri (author), Derner, Erik (author), Babuska, R. (author)

Many real-world systems can be naturally described by mathematical formulas. The task of automatically constructing formulas to fit observed data is called symbolic regression. Evolutionary methods such as genetic programming have been commonly used to solve symbolic regression tasks, but they have significant drawbacks, such as high...

journal article 2024

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Multi-Flow Generalization in Data-Driven Turbulence Modeling: An Exploratory Study

Hoefnagel, Kaj (author)

Computational fluid dynamics (CFD) is an important tool in design involving fluid flow. Scale-resolving CFD methods exist, but they are too computationally expensive for practical design. Instead, the relatively cheap Reynolds-averaged Navier-Stokes (RANS) approach is the industry standard, specifically models based on the Boussinesq hypothesis,...

master thesis 2023

document

Deep Symbolic Regression for Nonlinear Dynamical Systems

Thamban, Arun (author)

From the motion of electrons in an atom to the orbits of celestial bodies in the cosmos, governing equations are essential to the characterisation of dynamical systems. They facilitate an understanding of the physics of a system, which enables the development of useful techniques such as predictive control. An increasingly popular method to...

master thesis 2023

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Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression

Kubalik, Jiri (author), Derner, Erik (author), Babuska, R. (author)

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data. Historically, symbolic regression has been predominantly realized by genetic programming, a method that...

journal article 2023

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Mini-Batching, Gradient-Clipping, First-versus Second-Order: What Works in Gradient-Based Coefficient Optimisation for Symbolic Regression'

Harrison, Joe (author), Virgolin, Marco (author), Alderliesten, T. (author), Bosman, P.A.N. (author)

The aim of Symbolic Regression (SR) is to discover interpretable expressions that accurately describe data. The accuracy of an expression depends on both its structure and coefficients. To keep the structure simple enough to be interpretable, effective coefficient optimisation becomes key. Gradient-based optimisation is clearly effective at...

conference paper 2023

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Data-Driven Turbulence Modeling: Discovering Turbulence Models using Sparse Symbolic Regression

van Leeuwen, Elske (author)

Computational Fluid Dynamics (CFD) is the main tool to use in industry and engineering problems including turbulent flows. Turbulence modeling relies on solving the Navier-Stokes equations. Solving these equations directly takes a lot of time and computational power. More affordable methods solve the Reynolds Averaged Navier-Stokes (RANS)...

master thesis 2022

document

Data-Driven Turbulence Modelling of Algebraic Reynolds-Stress Models using Deep Symbolic Regression

Hemmes, Jasper (author)

When simulating fluids the industry standard is Reynolds averaged Navier-Stokes (RANS). However, the results for certain flows are inaccurate. The main source of error in popular RANS turbulence models is the Boussinesq approximation, assuming a linear relationship between the Reynolds stress anisotropy and the mean rate of strain. Experiments...

master thesis 2022

document

Bayesian deep learning for system identification

Zhou, H. (author)

Applying deep neural networks (DNNs) for system identification (SYSID) has attracted more andmore attention in recent years. The DNNs, which have universal approximation capabilities for any measurable function, have been successfully implemented in SYSID tasks with typical network structures, e.g., feed-forward neural networks and recurrent...

doctoral thesis 2022

document

Gene-pool Optimal Mixing in Cartesian Genetic Programming

Harrison, J. (author), Alderliesten, T. (author), Bosman, P.A.N. (author)

Genetic Programming (GP) can make an important contribution to explainable artificial intelligence because it can create symbolic expressions as machine learning models. Nevertheless, to be explainable, the expressions must not become too large. This may, however, limit their potential to be accurate. The re-use of subexpressions has the...

conference paper 2022

document

Evolvability degeneration in multi-objective genetic programming for symbolic regression

Liu, D. (author), Virgolin, Marco (author), Alderliesten, T. (author), Bosman, P.A.N. (author)

Genetic programming (GP) is one of the best approaches today to discover symbolic regression models. To find models that trade off accuracy and complexity, the non-dominated sorting genetic algorithm II (NSGA-II) is widely used. Unfortunately, it has been shown that NSGA-II can be inefficient: in early generations, low-complexity models over...

conference paper 2022

document

Hydraulic modelling of liquid-solid fluidisation in drinking water treatment processes

Kramer, O.J.I. (author)

In drinking water treatment plants, multiphase flows are a frequent phenomenon. Examples of such flows are pellet-softening and filter backwashing where liquid-solid fluidisation is applied. A better grasp of these fluidisation processes is needed to be able to determine optimal hydraulic states. In this research, models were developed, and...

doctoral thesis 2021

document

Data-driven RANS closures for three-dimensional flows around bluff bodies

Huijing, Jasper P. (author), Dwight, R.P. (author), Schmelzer, M. (author)

In this short note we apply the recently proposed data-driven RANS closure modelling framework of Schmelzer et al.(2020) to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at Re=40,000, and a cylinder at Re=140,000. For each flow, a new RANS closure is generated using sparse symbolic regression based...

journal article 2021

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Multi-objective symbolic regression for physics-aware dynamic modeling

Kubalík, Jiří (author), Derner, Erik (author), Babuska, R. (author)

Virtually all dynamic system control methods benefit from the availability of an accurate mathematical model of the system. This includes also methods like reinforcement learning, which can be vastly sped up and made safer by using a dynamic system model. However, obtaining a sufficient amount of informative data for constructing dynamic...

journal article 2021

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Symbolic Regression Methods for Reinforcement Learning

Kubalik, Jiri (author), Derner, Erik (author), Zegklitz, Jan (author), Babuska, R. (author)

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as neural networks or basis...

journal article 2021

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Selecting Informative Data Samples for Model Learning Through Symbolic Regression

Derner, Erik (author), Kubalik, Jiri (author), Babuska, R. (author)

Continual model learning for nonlinear dynamic systems, such as autonomous robots, presents several challenges. First, it tends to be computationally expensive as the amount of data collected by the robot quickly grows in time. Second, the model accuracy is impaired when data from repetitive motions prevail in the training set and outweigh...

journal article 2021

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Data­-driven techniques for finding governing equations of noisy nonlinear dynamical systems

Lingmont, Hidde (author)

The advent of machine learning and the availability of big data brought a novel approach for researchers to discover fundamental laws of motion. Computers allow to quickly find underlying physical laws from experimental data, without having in-depth knowledge of the system. Applications are widespread among numerous fields such as physics,...

master thesis 2020

document

Enhancement of data-driven turbulence models for wind turbine wake applications

Goderie, Michiel (author)

Wind turbine wakes cause significant reductions in power production and increased fatigue damage for downwind turbines. Thus, they affect the wind levelized cost of energy. Computational Fluid Dynamics (CFD) can be used to quantify the wake characteristics, whereby Reynolds-averaged Navier-Stokes (RANS) has the most potential for industrial...

master thesis 2020

document

Inferring algebraic stress models from high-fidelity data and applying machine learning to enhance and generalize turbulence lag models

Nieuwenhuisen, Kyle (author)

Adverse pressure gradients, separation and other forms of non-equilibrium flows are often encountered in flows of interest. In these type of flows, the Boussinesq hypothesis does not hold and often leads to erroneous predictions by eddy viscosity models. In an attempt to capture these non-equilibrium effects, lag parameter models introduce a lag...

master thesis 2020

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Symbolic regression of algebraic stress-strain relation for RANS turbulence closure

Schmelzer, M. (author), Dwight, R.P. (author), Cinnella, Paola (author)

In this work recent advancements are presented in utilising deterministic symbolic regression to infer algebraic models for turbulent stress-strain relation with sparsity-promoting regression techniques. The goal is to build a functional expression from a set of candidate functions in order to represent the target data most accurately....

conference paper 2020