Project description
Optimal computational methods for dynamic systems
In disciplines like computational physics, engineering, finance, or machine learning, accuracy without excessive computing is key. However, when it comes to time-dependent problems, existing methods often falter, unable to balance precision and efficiency. With this in mind, the ERC-funded OPTIMAL project aims to develop precise, yet computationally efficient, adaptive algorithms for these dynamic scenarios. Combining new mathematical insights with cutting edge computational tools, OPTIMAL seeks to revolutionise how we design and analyse adaptive algorithms. The goal is to develop provably optimal algorithms, ensuring unparalleled accuracy and efficiency in computational simulations. More than just pushing boundaries, OPTIMAL aims to redraw them, promising a transformative leap forward in the field.
Objective
The ultimate goal of any numerical method is to achieve maximal accuracy with minimal computational cost. This is also the driving motivation behind adaptive mesh refinement algorithms to approximate partial differential equations (PDEs).
PDEs are the foundation of almost every simulation in computational physics (from classical mechanics to geophysics, astrophysics, hydrodynamics, and micromagnetism) and even in computational finance and machine learning.
Without adaptive mesh refinement such simulations fail to reach significant accuracy even on the strongest computers before running out of memory or time.
The goal of adaptivity is to achieve a mathematically guaranteed optimal accuracy vs. work ratio for such problems.
However, adaptive mesh refinement for time-dependent PDEs is mathematically not understood and no optimal adaptive algorithms for such problems are known. The reason is that several key ideas from elliptic PDEs do not work in the non-stationary setting and the established theory breaks down.
This ERC project aims to overcome these longstanding open problems by developing and analyzing provably optimal adaptive mesh refinement algorithms for time-dependent problems with relevant applications in computational physics.
This will be achieved by exploiting a new mathematical insight that, for the first time in the history of mesh refinement, opens a viable path to understand adaptive algorithms for time-dependent problems. The approaches bridge several mathematical disciplines such as finite element analysis, matrix theory, non-linear PDEs, and error estimation, thus breaking new ground in the mathematics and application of computational PDEs.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- humanities history and archaeology history
- natural sciences physical sciences astronomy astrophysics
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-COG
See all projects funded under this callHost institution
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1040 Wien
Austria
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.