Related papers: Discovering Interpretable Physical Models using Sy…
Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work…
The partial differential equation (PDE) plays a significantly important role in many fields of science and engineering. The conventional case of the derivation of PDE mainly relies on first principles and empirical observation. However, the…
Referring expression comprehension (REC) aims to localize a target object in an image described by a referring expression phrased in natural language. Different from the object detection task that queried object labels have been…
Interpreting the impedance response of perovskite solar cells (PSCs) is challenging due to the complex coupling of ionic and electronic motion. While drift-diffusion (DD) modelling is a reliable method, its mathematical complexity makes…
In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra…
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…
Muscle-actuated organisms are capable of learning an unparalleled diversity of dexterous movements despite their vast amount of muscles. Reinforcement learning (RL) on large musculoskeletal models, however, has not been able to show similar…
Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…
The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an…
In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in…
Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary…
Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…
Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…
We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single phase flow is extended to simulate immiscible two-phase flows…
Modern Reinforcement Learning (RL) is more than just learning the optimal policy; Alternative learning goals such as exploring the environment, estimating the underlying model, and learning from preference feedback are all of practical…
PDE learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data. While deep learning models traditionally require copious amounts of training data, recent PDE learning…