Related papers: Questionnaires to PDEs: From Disorganized Data to …
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…
Diffusion models, widely used in image generation, rely on iterative refinement to generate images from noise. Understanding this data evolution is important for model development and interpretability, yet challenging due to its…
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…
Public data ecosystems (PDEs) represent complex socio-technical systems crucial for optimizing data use in the public sector and outside it. Recognizing their multifaceted nature, previous research pro-posed a six-generation Evolutionary…
Conditional Generative Models are now acknowledged an essential tool in Machine Learning. This paper focuses on their control. While many approaches aim at disentangling the data through the coordinate-wise control of their latent…
Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…
We develop data-driven models to predict the dynamics of a freely settling sphere in a quiescent Newtonian fluid using experimentally obtained trajectories. Particle tracking velocimetry was used to obtain a comprehensive dataset of…
Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and…
Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and…
Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal…
Solving time-dependent parametric partial differential equations (PDEs) remains a fundamental challenge for neural solvers, particularly when generalizing across a wide range of physical parameters and dynamics. When data is uncertain or…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Causal analyses of longitudinal data generally assume that the qualitative causal structure relating variables remains invariant over time. In structured systems that transition between qualitatively different states in discrete time steps,…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Recent advancements in deep learning have led to the development of various models for long-term multivariate time-series forecasting (LMTF), many of which have shown promising results. Generally, the focus has been on…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…