Periodic Reporting for period 4 - SpaTe (Spatio-Temporal Methods for Data-driven Computer Animation and Simulation)
Periodo di rendicontazione: 2025-03-01 al 2025-08-31
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.
We made substantial progress across all three scientific objectives of SpaTe. In particular, we developed new space–time representations and scalable surrogate models for complex physical dynamics, including transformer- and diffusion-based architectures and robust similarity metrics that characterize the structure of 4D simulation data.
In parallel, we advanced the project’s core vision of differentiable physics for inverse problems, releasing high-performance differentiable solvers (including a GPU-accelerated multi-block PISO solver), establishing stable long-horizon optimization techniques, and demonstrating unsupervised 4D reconstruction of flow fields from sparse observations. For unstructured and Lagrangian data, we introduced physically constrained particle-learning methods and symmetry-aware operators that form the basis for adaptive Lagrangian representations.
Across all lines, we created and disseminated open-source software, datasets, and benchmarking tools (e.g. differentiable turbulence models, APEBench, PDE-Transformer/P3D code bases), enabling broad adoption by the fluid-mechanics and machine-learning communities. Together, these contributions not only fulfil the scientific objectives of SpaTe but also establish strong foundations for next-generation simulation tools, data-driven design workflows, and hybrid AI-physics modelling approaches.
During the project, we disseminated our results widely across leading journals and conferences in machine learning, computational physics, and fluid mechanics. Our advances in space–time representations, stability analysis, and neural surrogate modelling were published at ICLR, ICML, NeurIPS, CMAME, NCAA, and related ML workshops. Our core contributions on differentiable solvers, turbulence modelling, and inverse problems appeared in top archival venues such as Journal of Fluid Mechanics, Journal of Computational Physics, Physical Review E, Computer Methods in Applied Mechanics and Engineering, as well as NeurIPS and ICLR for methodological breakthroughs. Our work on Lagrangian and unstructured data learning was disseminated through ICLR, NeurIPS (including an oral), and CVPR. Additionally, we released open benchmarks and tools (e.g. APEBench, PDE-Transformer, differentiable turbulence solvers) through NeurIPS, ICLR, ICML, and public code repositories, ensuring strong visibility, community uptake, and long-term impact.
In parallel, we advanced the project’s core vision of differentiable physics for inverse problems, releasing high-performance differentiable solvers (including a GPU-accelerated multi-block PISO solver), establishing stable long-horizon optimization techniques, and demonstrating unsupervised 4D reconstruction of flow fields from sparse observations. For unstructured and Lagrangian data, we introduced physically constrained particle-learning methods and symmetry-aware operators that form the basis for adaptive Lagrangian representations.
Across all lines, we created and disseminated open-source software, datasets, and benchmarking tools (e.g. differentiable turbulence models, APEBench, PDE-Transformer/P3D code bases), enabling broad adoption by the fluid-mechanics and machine-learning communities. Together, these contributions not only fulfil the scientific objectives of SpaTe but also establish strong foundations for next-generation simulation tools, data-driven design workflows, and hybrid AI-physics modelling approaches.
During the project, we disseminated our results widely across leading journals and conferences in machine learning, computational physics, and fluid mechanics. Our advances in space–time representations, stability analysis, and neural surrogate modelling were published at ICLR, ICML, NeurIPS, CMAME, NCAA, and related ML workshops. Our core contributions on differentiable solvers, turbulence modelling, and inverse problems appeared in top archival venues such as Journal of Fluid Mechanics, Journal of Computational Physics, Physical Review E, Computer Methods in Applied Mechanics and Engineering, as well as NeurIPS and ICLR for methodological breakthroughs. Our work on Lagrangian and unstructured data learning was disseminated through ICLR, NeurIPS (including an oral), and CVPR. Additionally, we released open benchmarks and tools (e.g. APEBench, PDE-Transformer, differentiable turbulence solvers) through NeurIPS, ICLR, ICML, and public code repositories, ensuring strong visibility, community uptake, and long-term impact.
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.