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Mathematical Sciences

Mathematical Sciences Research

Applied Geometry
Approximation Theory
Chemically-Reacting Flows
Computational Logic
Dynamical Systems
Environmental Problems
Fluid Dynamics
Inverse Problems
Machine Learning
Math Education
Mathematical Physics
Multiphase Flows
Nonlinear Analysis
Nonlinear Materials
Nonlinear Waves
Operations Research and Mathematical Programming
Perturbation Methods
Scientific Computing

Mathematical Sciences Research
Inverse Problems

Inverse problems are those in which the outcome is known, but the precise factors leading to the outcome are not known.

With inverse problems, scientists observe an effect and work to determine the cause. The ultimate goal is to find objects and their material or biological properties that cannot be directly measured.

Inverse Problems at Rensselaer

The field of inverse problems is a vast scientific area in which Rensselaer has a significant, high quality, well-established scientific base in the Inverse Problems Center. This center comprises distinguished researchers in such varied fields as mathematics, geosciences, and mechanical engineering.

In this exciting field, scientific challenges include:

  • Modeling of the physical problem.
  • Creating new mathematics for analysis of the model.
  • Identifying appropriate (often large) and/or rich data sets.
  • Working with scientific computations and visualization aids.
  • Undertaking experimental verification.

Current Projects

Researchers perform some projects at the most basic scientific level:

  • Find properties of the Earth’s substructure from seismic measurements.
  • Determine material properties of mechanical or biological systems.

Other problems focus on direct applications:

  • Establish the origin of contaminants measured in groundwater.
  • Find sediment properties of the seabed.
  • Locate objects concealed by vegetation cover.
  • Locate mines in the sea environment.
  • Find tumors in biological tissue.
  • Locate sources of hearth malfunction.
  • Distinguish abnormal from normal tissue.
  • Find temperature distributions in inaccessible regions.

In all these cases, it is either not possible or not desirable to make direct measurements.

Faculty Researchers

Joyce McLaughlin


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