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S-Computing Fundamentals Lab
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A lab that derives mathematically correct results while accounting for numerical computation errors.
AboutAbout the lab
Controlling the risks of numerical computation through verified computing.
The S-Computing Fundamentals Lab studies how to handle the inaccuracy and uncertainty of numerical computation and how to control the risks hidden in it.
The key is "verified numerical computation," a computational method that accounts for every error arising in numerical computation and uses it to derive mathematically correct results.
Using this method, the lab also works on "computer-assisted proofs," which carry out mathematical proofs on a computer.
On the website of Associate Professor Takayasu's lab, "TakLAB," the lab is introduced as a joint lab of three labs, including the Endo Lab and the Sato Lab, with "S-Computing Fundamentals Group" as its official name.
Key terms
- Verified numerical computation
- A computational method that accounts for every error arising in numerical computation and uses it to derive mathematically correct results
- Computer-assisted proof
- A method that uses verified numerical computation to carry out mathematical proofs on a computer
ResearchResearch themes
Numerical computation is used frequently in daily life, but using it incorrectly carries the risk of serious mistakes. Built on the three pillars of theory, practice, and implementation of verified numerical computation, the lab studies how to control the risks of numerical computation and how to develop computer-assisted proofs.
*Illustrative imageVerified computer-assisted proofs
The lab verifies the existence of connecting orbits in infinite-dimensional dynamical systems and numerically verifies invariant manifolds. It also develops general verified quadrature methods and works on computer-assisted proofs for the incompressible fluid equations.
*Illustrative imageNumerical verification of blow-up solutions
The lab determines blow-up times of differential equations and performs verified numerical computation of blow-up profiles. It also works on removing space-time singularities and on characterizing blow-up from a dynamical systems perspective by computing invariant manifolds.
*Illustrative imageApplications to hyperbolic partial differential equations
The lab takes up hyperbolic partial differential equations such as the advection equation and fluid equations. It applies the theory of verified numerical computation to systems of conservation laws, including the compressible fluid equations.
*Illustrative imageNumerical computation of the Keller-Segel system
The lab puts the theory of verified numerical computation into practice for reaction-diffusion systems. Its work covers verified numerical computation of radially symmetric solutions, clarifying the global structure of solutions, and the treatment of Neumann boundary conditions.
MembersFaculty
Members of the S-Computing Fundamentals Lab consist of faculty members and doctoral, master's, and undergraduate students.As of 2026
- ProfessorYasunori Endo
- Associate ProfessorAkitoshi Takayasu
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Servers in a Rack” Abigor / CC BY-SA 3.0 (cropped)
- Verified computer-assisted proofs: “Sun Microsystems Solaris computer cluster” ChrisDag / CC BY 2.0 (cropped)
- Numerical verification of blow-up solutions: “Mathematics, Lecture notes, Mathematical analysis, Linear algebra, Rostov-on-Don, Russia” Vyacheslav Argenberg / CC BY 4.0 (cropped)
- Applications to hyperbolic partial differential equations: “Schlieren photograph of T-38 shock waves” Leonard Weinstein / NASA / Public domain (cropped)
- Numerical computation of the Keller-Segel system: “Tiger Bush Niger Corona” US Agency / Public domain (cropped)
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- Related lab (新宅研究室): “MetalFatigue 001” National Institute of Standards and Technology / Public domain (cropped)
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