A PDE-informed optimization algorithm for river flow predictions

Author(s)

Birgin, E. G. ; Martinez, J. M.

• Document type: Journal article
• Source: NUMERICAL ALGORITHMS; v. N/A, p. 16-pg., 2023-09-07.

Abstract

An optimization-based tool for flow predictions in natural rivers is introduced assuming that some physical characteristics of a river within a spatial-time domain [x(min), x(max)] x[t(min), t(today)] are known. In particular, it is assumed that the bed elevation and width of the river are known at a finite number of stations in [x(min), xmax] and that the flow-rate at x = x(min) is known for a finite number of time instants in [t(min), t(today)]. Using these data, given t(future) > t(today) and a forecast of the flow-rate at x = x(min) and t = t(future), a regression-based algorithm informed by partial differential equations produces predictions for all state variables (water elevation, depth, transversal wetted area, and flow-rate) for all x. [x(min), x(max)] and t = t(future). The algorithm proceeds by solving a constrained optimization problem that takes into account the available data and the fulfillment of Saint-Venant equations for one-dimensional channels. The effectiveness of this approach is corroborated with flow predictions of a natural river. (AU)

• FAPESP's process: 18/24293-0 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants