{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:556"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:556","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Modeling complex systems with differential equations","abstract":"Mathematical models have since long been successful in describing nature
and specifically dynamical processes of real-world systems.
Solely relying on mathematical
formalism, it has become possible to make adequate predictions of
the temporal evolution of systems of all kind and furthermore to control
processes from outside.
However, despite the fact that mathematical models are more and more able
to describe processes on smallest and largest scales and theories
unify, it is not reasonable to try to describe all processes with one
formalism. On the contrary, mathematical models seem to
be confined to different levels of complexity since mathematical
approaches that work for small scales are not manageable in systems with
increasing complexity.
For example, quantum mechanics is well suited
for small scales,
however for describing the temporal evolution of macroscopic systems, the
quantum mechanical ansatz is not applicable not to
speak of even more complex systems. Similar to statistical mechanics,
respectively thermodynamics,
one is not interested in the behavior of the wave function of every
atom but in variables defining the system state on larger scales.
Departing from first principles and modeling mesoscopic or
macroscopic systems with 'appropriate' variables, often leads to the
situation where, for one system to be modeled, different mathematical
descriptions arise which are motivated from
first principles. One
then faces the situation where it is a priori unclear which
mathematical model is best suited to describe the system state and its
temporal evolution.
Additionally, through the approximative nature, these mathematical
models often contain unknown parameters
which cannot be derived from universal constants. This leads to the
so-called inverse problem where it is necessary to estimate unknown
parameters with help of experimental data. Beforehand it is additionally necessary to analyze identifiability of candidate models.","abstract_html":"Mathematical models have since long been successful in describing nature <br>and specifically dynamical processes of real-world systems. <br>Solely relying on mathematical <br>formalism, it has become possible to make adequate predictions of <br>the temporal evolution of systems of all kind and furthermore to control <br>processes from outside. <br>However, despite the fact that mathematical models are more and more able <br>to describe processes on smallest and largest scales and theories <br>unify, it is not reasonable to try to describe all processes with one <br>formalism. On the contrary, mathematical models seem to <br>be confined to different levels of complexity since mathematical <br>approaches that work for small scales are not manageable in systems with <br>increasing complexity. <br>For example, quantum mechanics is well suited <br>for small scales, <br>however for describing the temporal evolution of macroscopic systems, the <br>quantum mechanical ansatz is not applicable not to <br>speak of even more complex systems. Similar to statistical mechanics, <br>respectively thermodynamics, <br>one is not interested in the behavior of the wave function of every <br>atom but in variables defining the system state on larger scales. <br>Departing from first principles and modeling mesoscopic or <br>macroscopic systems with 'appropriate' variables, often leads to the <br>situation where, for one system to be modeled, different mathematical <br>descriptions arise which are motivated from <br>first principles. One <br>then faces the situation where it is a priori unclear which <br>mathematical model is best suited to describe the system state and its <br>temporal evolution. <br>Additionally, through the approximative nature, these mathematical <br>models often contain unknown parameters <br>which cannot be derived from universal constants. This leads to the <br>so-called inverse problem where it is necessary to estimate unknown <br>parameters with help of experimental data. Beforehand it is additionally necessary to analyze identifiability of candidate models.","abstract_has_math":false,"creators":["Müller, Thorsten"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Honerkamp, Josef"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:21:46Z","subjects":["Modellselektion","Parameterschätzung","Identifizierbarkeit","Model selection","data analysis","dynamical systems","parameter estimation","identifiability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/556","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Honerkamp, Josef"]},{"key":"dc:creator","label":"Author","values":["Müller, Thorsten"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Modellselektion","Parameterschätzung","Identifizierbarkeit","Model selection","data analysis","dynamical systems","parameter estimation","identifiability"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Mathematical models have since long been successful in describing nature
and specifically dynamical processes of real-world systems.
Solely relying on mathematical
formalism, it has become possible to make adequate predictions of
the temporal evolution of systems of all kind and furthermore to control
processes from outside.
However, despite the fact that mathematical models are more and more able
to describe processes on smallest and largest scales and theories
unify, it is not reasonable to try to describe all processes with one
formalism. On the contrary, mathematical models seem to
be confined to different levels of complexity since mathematical
approaches that work for small scales are not manageable in systems with
increasing complexity.
For example, quantum mechanics is well suited
for small scales,
however for describing the temporal evolution of macroscopic systems, the
quantum mechanical ansatz is not applicable not to
speak of even more complex systems. Similar to statistical mechanics,
respectively thermodynamics,
one is not interested in the behavior of the wave function of every
atom but in variables defining the system state on larger scales.
Departing from first principles and modeling mesoscopic or
macroscopic systems with 'appropriate' variables, often leads to the
situation where, for one system to be modeled, different mathematical
descriptions arise which are motivated from
first principles. One
then faces the situation where it is a priori unclear which
mathematical model is best suited to describe the system state and its
temporal evolution.
Additionally, through the approximative nature, these mathematical
models often contain unknown parameters
which cannot be derived from universal constants. This leads to the
so-called inverse problem where it is necessary to estimate unknown
parameters with help of experimental data. Beforehand it is additionally necessary to analyze identifiability of candidate models."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf","application/x-zip-compressed"]},{"key":"dc:title","label":"Title","values":["Modeling complex systems with differential equations","Modellierung komplexer Systeme mit Differentialgleichungen"]}]}],"canonical_facts":{"dc:contributor":["Honerkamp, Josef"],"dc:creator":["Müller, Thorsten"],"dc:description.abstract":["Mathematical models have since long been successful in describing nature
and specifically dynamical processes of real-world systems.
Solely relying on mathematical
formalism, it has become possible to make adequate predictions of
the temporal evolution of systems of all kind and furthermore to control
processes from outside.
However, despite the fact that mathematical models are more and more able
to describe processes on smallest and largest scales and theories
unify, it is not reasonable to try to describe all processes with one
formalism. On the contrary, mathematical models seem to
be confined to different levels of complexity since mathematical
approaches that work for small scales are not manageable in systems with
increasing complexity.
For example, quantum mechanics is well suited
for small scales,
however for describing the temporal evolution of macroscopic systems, the
quantum mechanical ansatz is not applicable not to
speak of even more complex systems. Similar to statistical mechanics,
respectively thermodynamics,
one is not interested in the behavior of the wave function of every
atom but in variables defining the system state on larger scales.
Departing from first principles and modeling mesoscopic or
macroscopic systems with 'appropriate' variables, often leads to the
situation where, for one system to be modeled, different mathematical
descriptions arise which are motivated from
first principles. One
then faces the situation where it is a priori unclear which
mathematical model is best suited to describe the system state and its
temporal evolution.
Additionally, through the approximative nature, these mathematical
models often contain unknown parameters
which cannot be derived from universal constants. This leads to the
so-called inverse problem where it is necessary to estimate unknown
parameters with help of experimental data. Beforehand it is additionally necessary to analyze identifiability of candidate models."],"dc:format.medium":["application/pdf","application/x-zip-compressed"],"dc:subject":["Modellselektion","Parameterschätzung","Identifizierbarkeit","Model selection","data analysis","dynamical systems","parameter estimation","identifiability"],"dc:title":["Modeling complex systems with differential equations","Modellierung komplexer Systeme mit Differentialgleichungen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:46Z"}