Periodic Reporting for period 3 - SpaTe (Spatio-Temporal Methods for Data-driven Computer Animation and Simulation)
Okres sprawozdawczy: 2023-09-01 do 2025-02-28
This grant project aims for a fusion of space-time physics with machine learning algorithms that will allow us to fundamentally improve the way we work with computer simulations, and benefit forward as well as inverse problem solvers with physical constraints. More informally, the goal of "SpaTe" is to develop new classes of data-driven spatio-temporal methods and demonstrate their potential to drive the next generation of numerical simulations.
It consists of three parallel and synergistic lines of work:
1) Target learning generic and re-usable representations based on neural networks that target grid-based space-time functions of physical problems.
2) Employ advanced numerical techniques for discretizing the differential operators of model equations to arrive at robust, unsupervised learning algorithms for physical phenomena.
3) Develop adaptive algorithms for sparse, point-based space-time functions to analyze and disambiguate complex data sets such as point clouds without correspondences.
It consists of three parallel and synergistic lines of work:
1) Target learning generic and re-usable representations based on neural networks that target grid-based space-time functions of physical problems.
2) Employ advanced numerical techniques for discretizing the differential operators of model equations to arrive at robust, unsupervised learning algorithms for physical phenomena.
3) Develop adaptive algorithms for sparse, point-based space-time functions to analyze and disambiguate complex data sets such as point clouds without correspondences.
In the first two periods of this project, we have focused on milestones A and B for all 3 lines of work outlined in the grant proposal. More specifically, we have continually worked on improving reduced temporal representations (1.A) new algorithms for physics based inverse problems solvers (2.A) and improved learning for Lagrangian representations (3.A). In addition, we are now working on space-time invariants for improved learning, (2.A) multi-level algorithms (2.B) and adaptivity for Lagrangian representations (3.B).
We have successfully published a series of paper on these topics which significantly advance the state of the art. Among others, we have worked on optimizing shapes immersed in a flow with learned surrogates, we have published learned turbulence model using a differentiable solver, and a method to improve conservation of momentum for Lagrangian simulations. More recent publications are likewise noteworthy: e.g. one of them targets the physical reconstruction of smoke phenomena with physical learning, and has been successfully published at the renowned CVPR conference, another paper proposed the half-inversion of gradients for deep learning, and was published at ICLR. A central building block of our project, a differentiable second-order solver for learning turbulence models, was successfully published at the renowned Journal of Fluid Mechanics (JFM).
In addition, a side track of our work was by now successfully published in a generic machine learning venue. It proposes the use of bi-directional losses for improved feature extraction in neural networks.
We are currently starting work on the final section of milestones of the three directions of our grant proposal: transfer learning for physics simulations (1.C) unsupervised reconstructions (2.C) and recurrent Lagrangian algorithms (3.C).
We have successfully published a series of paper on these topics which significantly advance the state of the art. Among others, we have worked on optimizing shapes immersed in a flow with learned surrogates, we have published learned turbulence model using a differentiable solver, and a method to improve conservation of momentum for Lagrangian simulations. More recent publications are likewise noteworthy: e.g. one of them targets the physical reconstruction of smoke phenomena with physical learning, and has been successfully published at the renowned CVPR conference, another paper proposed the half-inversion of gradients for deep learning, and was published at ICLR. A central building block of our project, a differentiable second-order solver for learning turbulence models, was successfully published at the renowned Journal of Fluid Mechanics (JFM).
In addition, a side track of our work was by now successfully published in a generic machine learning venue. It proposes the use of bi-directional losses for improved feature extraction in neural networks.
We are currently starting work on the final section of milestones of the three directions of our grant proposal: transfer learning for physics simulations (1.C) unsupervised reconstructions (2.C) and recurrent Lagrangian algorithms (3.C).
All projects mentioned above have successfully improved the state of the art in their respective areas. E.g. the Lagrangian method outlined above outperforms existing continuous convolutions and graph networks by a significant margin in terms of end point errors.
In the longer term, we expect that this project will allow us to better understand the physical world around us. It will help us to analyze sparse and ambiguous measurements such as videos and 3D scans automatically and reliably, with a vast range of practical applications from social-media apps to autonomous vehicles.
In the longer term, we expect that this project will allow us to better understand the physical world around us. It will help us to analyze sparse and ambiguous measurements such as videos and 3D scans automatically and reliably, with a vast range of practical applications from social-media apps to autonomous vehicles.