Seminar on Computational Learning and
Adaptation
Discovery of Partial Differential Equations:
A Declarative Bias Approach
Ljupco Todorovski
Jozef Stefan Institute
Ljubljana, Slovenia
www-ai.ijs.si/~ljupco/
This talk focuses on discovery of partial differential equations,
which are one of the most powerful and widely accepted analytical
formalisms for modeling biological and physical systems. Establishing
an acceptable partial differential equation model from example behavior
of the dynamic system has two main aspects. First, an appropriate
structure must be determined for the equations involved (the problem
of model identification). Second, accurate values of the constant
parameters must be determined (the problem of parameter estimation).
We focus on the first, more challenging, aspect of modeling, drawing on
the system Lagramge, which uses a declarative bias approach to equation
discovery. Instead of exploring a fixed (hard-coded) space of possible
equation structures, Lagramge uses a context-free grammar to define
and restrict its hypothesis space. The context-free grammar is provided
by the user and is based on theoretical knowledge about the domain.
We demonstrate the efficacy of this approach by its rediscovery of the
classic FitzHugh-Nagumo model from biology. This represents a very wide
class of biological systems, making the equation discovery of interest
to scientists concerned with the enterprise of obtaining a mathematical
understanding of dynamic processes that occur in the life sciences.
Date: Thurs., Oct 5
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Time: 4:15-5:30PM
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Place: Cordura 100
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