Optimering under osäkerhet

grafik över grafer och statistik

En matematisk modell av ett verkligt system kan bara vara så bra som den underliggande datan. Därför strävar vi efter att integrera datadriven information för att förbättra befintliga optimeringsmodeller och undersöka hur deterministiska modeller kan skyddas mot påverkan från osäker data.

Att överbrygga klyftan mellan teori och praktik kan vara utmanande. Även om matematiska modeller ofta kan fånga de viktigaste egenskaperna hos naturliga eller människoskapade komplexa system, beror deras precision på noggrannheten i de valda modellparametrarna. Tyvärr är dessa parametrar i sig känsliga för fel, såsom mätfel vid inflödet av material i en reaktor eller variationer i produktionen av förnybar energi på grund av väderförhållanden. Dessutom kan de härstamma från illvilligt beteende, till exempel om data som matats in i modellen har blivit korrupt genom en cyberattack.

Det är därför av avgörande betydelse att indata bedöms med stor omsorg, och om det finns tvivel kring dess noggrannhet, bör optimeringsmodellen vara medveten om och motståndskraftig mot potentiella felaktigheter. För att bidra till detta arbete fokuserar vi på två huvudsakliga forskningsinriktningar:

Datadriven optimering

Å ena sidan strävar vi efter att använda moderna verktyg inom datavetenskap, såsom (oövervakad och övervakad) inlärning, särskilt via neurala nätverk, för att samla datadriven information om de aktuella egenskaperna. Därefter integrerar vi denna information i klassiska optimeringsmodeller. Detta möjliggör ofta att fånga egenskaper som är svåra att modellera med traditionella metoder, men det innebär också att den erhållna informationen kan vara osäker och måste granskas kritiskt. Denna granskning kan ske inom optimeringsdisciplinen, exempelvis genom robustifiering, eller tvärvetenskapligt, genom experimentell verifiering. Tillämpningar inkluderar bildigenkänning eller effektiv drift av elsystem.

Robust optimering

Å andra sidan strävar vi efter att fånga osäkerheter i parametrar inom befintliga deterministiska modeller och integrera information om deras fördelning. Det finns två huvudsakliga forskningsfrågor inom detta område:

  • Hur kan vi fatta beslut som är robusta mot negativa scenarier?
  • Hur kan vi effektivt anpassa oss till ett specifikt urval av scenarier?
  • Ur ett spelteoretiskt perspektiv kan båda frågorna ses som två spelare som spelar mot varandra; i första frågan gör beslutsfattaren det första draget och i andra frågan gör en potentiell motspelare det första draget. Denna struktur förekommer inom en mängd olika områden, och har därför tillämpningar inom diskret geometri, kemiteknik, elektroteknik och logistik – för att nämna några.

Pågående projekt

(In English)

Production optimisation for hydroelectric power plants - Stochasticity and water head dependencies

Background

Hydropower is an important part of the flexibility of the power system. The ability to plan the dimensioning of hydropower, as well as its short-term and long-term operation, has a direct impact on the possibilities to act flexibly. With more reliable models, it becomes easier to predict how much one can and wants to produce at a given time, and to assess future capacity. The following shortcomings have been identified in current calculation models.

  • Existing calculation models for hydropower production that include stochasticity, for example uncertainty regarding future water flow (levels in water reservoirs, precipitation) and forecast models for the electricity price market, are too computationally intensive to be used in the analysis of entire river systems (for example the Lule River).
  • Today, the effect of head (or reservoir levels) on the ratio between turbine water flow and produced electrical power is taken into account in models for hydropower production planning, in order to reduce calculation times.

 

PhD project

Existing optimization models that take head into account are far too complex to be truly useful for larger river systems — especially when applied to long-term studies when uncertainties must be taken into account in different ways. Vattenfall AB sees great value in developing such models, as it provides better planning conditions, leads to better profit margins and enables more stable operation of their plants.

  • The project aims to develop mathematical models that take head dependence and stochasticity into account, and to develop efficient solution methods that can calculate solutions within practically usable time frames, even for entire river systems.
  • A combination of scientific disciplines is necessary (expertise in flow dynamics, hydropower, simulation and optimization theory).
  • Modeling stochasticity and uncertainty leads to the research areas of stochastic optimization and robust optimization, both of which are active research areas.
  • To succeed in keeping computation times down, significant method development will be required, utilizing problem knowledge and model structures.

 

E-Charge 2 - Accelererated transition towards emission free long haul truck transports

Purpose and goal

The purpose of the project is to contribute to an accelerated transition to a future logistics system that meets the national requirements to reduce emissions from domestic transportation. The project will describe, build and demonstrate the transport ecosystem consisting of electrified long-distance (or energy-intensive) truck transports that require high-power charging in order to understand and develop a basis for how Sweden can accelerate the transition to an emission-free logistics system.

Expected effects and result

The project has the ambitious goal of putting 200 trucks in electrified long-distance transport in commercial operation as early as 2027, which is a prerequisite for the continued rollout towards 3,000 vehicles in 2030. It will contribute to the expansion of critical MCS charging infrastructure and results and effects are expected to have a wide geographical scope. Over time, the results and effects will contribute to the development of sustainable transport solutions on a global scale.

Planned approach and implementation

The project adopts a systems engineering approach and is structured with vertical and horizontal work packages. A large number of logistics actors will develop, demonstrate and validate efficient electrified logistics flows. Experiences from these arrangements are then utilized in horizontal work packages with the goal of developing, in collaboration with all project parties, documentation regarding FFI´s five system dimensions in order to prepare the market for these types of vehicles.

 The project duration is November 2024 to December 2027. 

Read more about the Vinnova project

Improved image reconstruction of electrocatalytic surfaces via data-driven optimization

Research question

This project aims to leverage data-driven methods to visualize electrochemical changes in materials at the nanometer scale, supporting the design of electrocatalysts for sustainable technologies such as water splitting and CO₂ utilization. Improving electrocatalytic activity and selectivity in oxygen reactions (OER/ORR) requires modifying the catalyst surface—specifically reducing the native oxide layer and forming a new, controlled oxide layer.

Although in operando Transmission Electron Microscopy (TEM) can visualize these processes, frame-by-frame analysis is time-consuming, and signal loss in liquid electrolytes limits resolution. To address this, we propose enhancing compressed sensing algorithms using prior imaging data and model knowledge. A deep neural network will be trained to identify characteristic features of electrocatalytic surfaces, guiding the reconstruction of high-quality TEM visualizations in real time.

Sustainability aspects

Technology based on direct conversion between chemical and electrical energy is crucial for a sustainable society and to reduce global warming. Electrochemical water splitting and recombination or CO2 utilization is key for electrolysers and fuel cells. However, current catalysts for oxygen reactions rely on scarce, expensive platinum group metals (e.g., Ir, Ru), limiting scalability. We have developed thin film electrocatalysts based on transition metals as a sustainable alternative. Modifying the native oxide layer is essential to expose active sites and enhance performance. Additionally, the process allows for post-use catalyst recovery. This project will develop a reconstruction model for TEM micrographs to visualize the formation and evolution of surface oxides and oxide particles, supporting the development of cost-effective, high-performance catalysts.

Project-related publications

Globally solving unbalanced Gromov-Wasserstein problems in low dimensional Euclidean spaces

Improving reconstructions in nanotomography for homogeneous materials via mathematical optimization

More information

Read more about the WISE-WASP project

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