METHODOLOGICAL RESEARCH:
* Forecasting (PP)
Short:
Methodological developments related to forecasting encompass statistical
modeling aspects, communication of the forecasts, and subsequent decisionmaking.
Long:
The ultimate objective of any kind of mathematical modeling is to have the ability
to forecast the future behavior of the system considered. This is thus also the
case when developing statistical models. Forecasting is however a peculiar
research area, since developing a model describing the observed behavior of a
system, may not be enough for insuring sufficient forecast ability. For instance,
understanding how and why oil prices increased so suddenly in the last few
years is certainly not enough for forecasting when will be the next time this will
happen. Forecasting can then be seen as a combination of mathematical
modeling and expert knowledge. Methodological research related to forecasting
includes probabilistic forecasting, extreme event detection (and issuing of
warnings/alarms), etc.
While forecasting is common when talking about the weather, oil prices or more
generally stock exchange markets, few may know that forecasting is also
necessary for a wide range of industrial applications (eg. production and
maintenance management, transportation planning, product development), as
well as social and political issues. Optimal decision-making is today generally
based on forecasts. Methodological developments therefore also include optimal
communication of forecasts, and stochastic decision-making.
* Data Assimilation (PP)
Short:
Development in the field of data assimilation focuses on nonparametric Bayesian
methods such as particle filtering.
Long:
Data assimilation is the process of accounting for new data, describing the state
of a system, for the initialization (or recalibration) of a mathematical model
describing the evolution of such a system. The most known areas using data
assimilation are weather and hydrological forecasting, for which analysis cycles
permit to regularly update the estimated state of the atmosphere and oceans.
Approaches to data assimilation may range from simple spatial interpolation
techniques to more complex recursive Bayesian estimation techniques. The most
famous of those approaches is certainly Kalman filtering, related to which
significant research developments are still on the way (eg. ensemble Kalman
filtering), and which has a broad range of applications for system modeling,
forecasting and control. Today, research efforts at DTU Informatics concentrates
on newly developed methods such as particle filtering for instance.
* Modelling using Stochastic Differential Equation (LEC)
Short:
Stochastic differential equations are used to describe many systems with true
noise and simplified models. Its application opens for a wide range of tools for
model building and selection.
Long:
Stochastic differential equations (SDEs) are used within many fields to model
systems that are too complex to be described perfectly using ordinary differential
equations and for systems with noise. One of the advantages relative to ordinary
differential equations (ODEs) is that it is possible to separate measurement noise
from system noise and hence gaining more insight into the origin of the noise. A
large part of the work on SDEs at DTU Informatics is related to discretely
observed continuous time stochastic state space models. Allowing for parameter
estimation in a likelihood framework. And using likelihood ratio tests for model
comparison.
The group currently have two software packages within these topics: CTSM
(www.imm.dtu.dk/~ctsm) and PSM (www.imm.dtu.dk/projects/psm) where the
latter is expected to replace CTSM as it is further developed.
Topics of interest include the use of additional random walk states in suggesting
functional relationships, methods for model evaluation, and estimation of linear
and non-linear mixed-effects models using stochastic differential equations.
* Model Evaluation (PP og LEC)
Short:
Model evaluation is one of the kernels of the statistical methodology, and is
fundamental for model building, hypothesis checking, and for the forecasting
application.
Long:
While model evaluation may be seen in an engineering sense as a simple check
of the fitting of a model to observation data, the overall statistical framework of
model evaluation is much more complex. It may involve the combined use of a
number of statistical criteria permitting to balance model fit and complexity. It
may also translate to hypothesis testing…
When considering the forecasting application for nonlinear processes, model
evaluation requires the developments of complete frameworks permitting to
assign a level of quality to the forecasting models developed, but also to point
towards weaknesses of existing models and necessary future developments.
Especially in the young field of probabilistic forecasting, researchers at DTU
Informatics are active in proposing evaluation methods and frameworks.
* Modelling of Spatial and Spatio-temporal Processes (LEC og PP)
Short:
Some processes require the development of specific spatial or spatio-temporal
approaches. This may involve clustering, spatial smoothing (kriging), and spatiotemporal dynamic modeling
Long:
Importance of focusing on spatial processes has been stressed by geosciences
few decades ago. However now, it is recognized that complete methodologies
have to be developed for spatial and spatio-temporal processes, beyond the sole
application of geosciences. Applications may range for weather or climate
modeling, to pollution and disease spreading, and even to wind power forecast
uncertainty.
For such processes, dimension reduction aspects are crucial in view of the
potential size of datasets considered. In parallel, simultaneous consideration of
both spatial and temporal components may require the proposal of new filtering
techniques, semi-parametric and non-parametric frameworks to spatial
covariance modeling, and new types of dynamical models applied to lattices.
* Nonlinear and Nonparametric Methods in Time Series Analysis (PP og
LEC)
Short:
Improving models and methods for time series analysis requires constant
developments, which may derive from eg. new regression methods, varyingcoefficient models, regime-switching concepts, or mixtures of models.
Long:
In contrast to linear time-series analysis which is a fairly established area,
nonlinear time-series analysis still requires the proposal of new models and
development of new methodologies. Forgetting about linearity and the Gaussian
assumption requires new ways of conceiving the statistical methodology. This
translates to the development of data-driven (nonparametric) approaches to
regression and estimation, data transformation aspects, new correlation
concepts, etc. These new statistical modeling techniques are then applied to a
wide range of practical problems, for which they prove their superiority in terms of
model fitting, resulting forecast accuracy, and in their ability to explain the
underlying processes.
APPLIED RESEARCH:
* Wind Power Forecasting (PP)
Short:
Wind power forecasting is a significant area of expertise at DTU Informatics,
which research efforts concentrated on forecasting at different time scales, and
optimal decision-making (management, trading, maintenance planning) based on
forecasts.
Long:
Wind power generation is a nonlinear and bounded process. In addition, the fact
that wind generation is directly related to wind speed, the characteristics of this
process are constantly – though slowly – changing with time: it may be seen as
nonstationary. All these aspects make the forecasting of wind power generation a
complex task, whatever the time-scale considered (ie. from few minutes to few
days ahead). Today, wind power forecasting is recognized as a research field of
its own, with connections to meteorology, mathematical modeling, and power
system engineering. Forecasts of wind generation are used on a daily basis by
wind power producers, energy traders, maintenance planners, regulating
authorities, etc. As wind generation takes a more and more significant part of the
electricity mix, using forecasts will become a basis to decision-making
A specificity of wind power generation is its highly volatile and hardly predictable
nature. In addition, many researchers have shown that optimal decisions in terms
of trading or management of wind power cannot be made from a single forecast
only. This is the reason why a large part of research efforts are focused on
probabilistic forecasting (see Figure below), spatio-temporal aspects of forecast
uncertainty, and stochastic decision-making.
At DTU Informatics, the research related to the wind power application deals with
these various topics:
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Point forecasting of wind power (for horizons from few minutes to several
days ahead)
Spatio-temporal modeling of wind generation at the level of a region or a
country (as well as the forecast uncertainty)
Probabilistic forecasting of wind power (up to few days ahead): quantile
forecasting, prediction intervals and density forecasts, or alternatively
scenarios
Skill forecasting, indicating the confidence to have in provided forecasts
* Electricity Price Forecasting (PP)
Short:
The research on electricity price forecasting mainly focuses on aspects related to
the effects of stochastic generation on electricity prices and competitive bidding.
Long:
The liberalization of electricity markets, especially in Scandinavian countries, has
led to certain changes in the way electricity is traded. In addition, the significant
share of renewable energies such as wind and hydro power with their inherent
characteristics, results in external forces acting on the electricity prices.
Trading power generation via liberalized electricity markets makes the value of
each unit of produced energy tightly linked to the variations of prices in the
various electricity markets. And, if focusing on renewable generation such as
wind power for instance, the final revenue on the market may then be a complex
function of revenues on markets with different gate closures (day-ahead, intraday, etc.) and of the penalties coming from non-respect of settled bids. While
forecasting of renewable generation is crucial for trading, it is also important to be
able to forecast prices on the various markets, accounting for the potential
influence of external factors.
In that context, research at DTU Informatics puts emphasis on the following
issues:
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Forecasting of prices on spot, intraday, and regulation markets, accounting
for the influence of wind generation on such electricity prices
Probabilistic forecasting of prices and penalties, in order to seize their
uncertainty
Modeling of the interaction of stochastic generation sources with the
various markets
Stochastic decision-making methods, ie. stochastic optimization or
stochastic programming, in order to design optimal management and
trading strategies
Possibly stochastic decision-making methods accounting for combined
systems eg. wind-storage, wind-hydro, or wind -CHP
* Financial Modelling (HM)
Short:
Long:
* Pharmaceutical (PK/PD) Modelling (LEC et al.)
Short:
Development of new drugs involves many experiments and including very costly
clinical trials. So proper modelling of pharmacokinetics and pharmacodynamics is
an important tool increasing the knowledge gain from the experiments.
Long:
Missing – I guess Søren and Stig should contribute here ...
* Bacterial Growth and Evolution Modelling (LEC)
Short:
The main focus is on using stochastic mathematical modelling to acquire new
insights in bacterial life in collaboration with microbiologists.
Long:
Selection of bacteria happens all the time. Bacteria mutate and adjust to the
environment also when exposed to antimicrobial agents such as antibiotics.
Doctors, microbiologists, and epidemiologists produce and gather data that is
important in describing these processes. One of our main focuses is to use this
data in model development and thereby through close collaboration acquire new
insights into bacterial growth and evolution.
Traditionally these systems are modelled using ordinary differential equations
thereby implicitly assuming that the model is perfect – however these models
only approximates the complex life of bacteria and thus we focus on applying
stochastic differential equations and stochastic simulation models instead.
Examples of the cases we work with include modelling:
 Adaptation of P. aeruginosa to ciprofloxacin – an important antibiotic in
many treatments including cystic fibrosis patients.
 Competition between different bacteria when exposed to antimicrobial
agents such as detergents and conservatives – does the disease causing
bacteria win?

* Environmental Modelling (JKL kan få JKM til at skrive)
Short:
Long:
Real life ecosystems nature complex dynamic system and measurements of
these systems are often difficult and expensive, as a consequence data are often
few and noisy. Different components of ecosystems are often characterized by
different time-constant, an example from the ocean is that algae might double
within hours or days, whereas eelgrass covering the seabed uses years or
decades. These timescales should be covered in models which capture the
interactions between species, because of the complexity of the systems
statistical rather than mechanistic methods are needed described these systems.
In the above example a question that should be answered could be, how much
pressure in terms of nutrient (from agriculture and cities) can a marine ecosystem
absorb and remain healthy? The answer to this question should be given in a
statistical sense, that is we should be able to give an estimate of the risk of a
break down. The Kalman filter and the extended Kalman filter provide tools for
reconstructions of the state of a system, and provide an estimate of the variance
of the point estimate, the assumption in this filtering problem is however that
noise is additive and Gaussian. For biological systems it is however known that
noise very often scale with the number of individuals or amount of biomass. To
describe this behavior noise should be multiplicative and non-Gaussian, a natural
choice for the distribution is the log-normal distribution. How to include such
models in Kalman filter like set up is however not part of the standard toolbox,
and techniques for handling this is under development.
The challenge described above apply for discrete time models as well as for
Stochastic Differential Equation (SDE) models. In addition to scale dependent
noise realistic models for ecosystems will often involve highly nonlinear terms like
thresholds, and the behavior of non-linear stochastic models can differ
significantly from the deterministic skeleton of the stochastic models.
* Population modeling (MWP + LEC)
Short:
Our research includes models for spread of disease and tracing animals, e.g.
fish.
(Skal omformuleres)
Long:
Spatially explicit simulation models for exotic diseases such as foot and mouth
disease, swine pest, and blue tongue are important both for increasing the
preparedness while waiting for the arrival and for evaluating the effect of possible
interventions and changes in the regulation, e.g. animal movement restrictions
and use of vaccines. One of our challenges is how to maximize the benefit of the
additional data that is collected in Denmark.
(Mere hvis MWP skal med)
* Well Field Modelling (JKL kan få Fannar til at skrive)
Short:
Long:
Well field modelling refers to models for groundwater flow, penetrated by wells
for infiltration and/or discharge from corresponding aquifer, combined with a
water distribution model. The physical model of groundwater flow is essentially
described by partial differential equation, which considers the water elevation in
the aquifer in both time and space. The measurement error between the model
and the measurements from the operating wells in the field needs to be reduced
for the model to be adequate for both simulation and prediction of the
groundwater system. Therefore, the groundwater flow equation is formulated in a
stochastic dynamic framework, such that the model is corrected to sufficiently
reflect the real-time monitoring management system. The core of this framework
consist of stochastic differential equations, or so-called grey box models since
derived for the well field system to combine physical knowledge (referred to as
white box models) and information in observed data series (black box).
DTU Informatics, mathematical statistics, participates in the research project
Wellfield Optimization, which includes development and integration of modelling,
data assimilation, optimization, control, and sensor technologies into a real-time
well field operation and management system. An integrated, dynamically coupled
hydrological and hydraulic well field modelling system is developed for modelling
the flow of water from the aquifer to the waterworks. More interesting and
informative details on well field optimization can be found on the project website:
http://wellfield.dhigroup.com.
* Modelling and Forecasting for District Heating Systems (PP)
Short:
District heating is a specificity of Scandinavian countries, the optimal
management of which requires advanced nonlinear models of the network
dynamics, for forecasting and control purposes.
Long:
Owing to the importance of district heating in the Northern European countries,
the group also focuses on modeling and prediction problems in central district
heating systems. The final objective when considering this problem is, given
fluxes and temperature losses in the network, but also the consumption pattern
of water consumers, to optimize the water flux and temperature at the central
water supply point. For that purpose, it may necessary to forecast both loads and
water temperature at critical points of the district heating network.
The research works at DTU Informatics concentrate on:
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Load forecasting
Nonlinear modeling of the dynamics of the networks (see Figure below)
Forecasting of the temperature at critical points
Model Predictive Control (MPC) by embedding forecasts in existing
controllers implemented at the supply point
* Modelling of Thermal Dynamical Systems (HM)
Short:
Long:
Building energy signature, PV system modeling, etc.