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Partial Differential Equations and Calculus of Variations Lab
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The lab explores the behavior of materials and molecules using partial differential equations and the calculus of variations.
AboutAbout the lab
Using mathematics to study the properties of materials and molecules
The Partial Differential Equations and Calculus of Variations Lab investigates problems in elasticity theory and functional materials, building on partial differential equations and vector-valued calculus of variations.
Its research includes mathematically modeling defects that arise in crystal lattices and using machine learning to study the properties of molecules.
The lab also studies anomalies that appear in blockchain transactions.
Professor Pierluigi Cesana is also a faculty member of the Department of Mathematics in the Graduate School of Mathematics and of the Graduate School of Mathematics for Innovation.
Key terms
- Partial differential equation
- An equation describing how a quantity changes depending on multiple variables
- Calculus of variations
- A mathematical method for finding the state in which a quantity such as energy is minimized
- Disclination
- A defect in a crystal lattice caused by an angular mismatch
- Molecular fingerprint
- A representation of a molecule's structural features as a sequence of numbers
ResearchResearch themes
The lab studies problems of functional materials and molecules using partial differential equations, vector-valued calculus of variations, and data-driven methods from machine learning and AI. Its research themes include effective molecular descriptors, anomaly detection in blockchain transactions, graphene design, and AI-based design of functional molecules.
*Illustrative imageRepresenting Molecular Features
The lab studies effective molecular descriptors. Using molecular fingerprints, data science, and deep learning, it works with molecules in organic chemistry.
*Illustrative imageAnomaly Detection in Blockchain Transactions
The lab models and studies anomalies that appear in transactions on blockchain networks. Through transaction analysis and anomaly detection, it addresses blockchain security.
*Illustrative imageFunctional Design of Graphene
The lab studies new mathematical approaches for designing graphene toward specific functions. It treats dislocation defects and disclinations with continuum mechanics, and also uses density functional theory and machine learning.
*Illustrative imageAI-Based Design of Functional Molecules
The lab works on designing and optimizing functional molecules with AI. It uses methods such as quantum chemistry, machine learning, deep learning, and genetic algorithms.
MembersFaculty
- ProfessorPierluigi Cesana
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: “Graphene g-C3N4” Vicente Neto / CC BY 4.0 (cropped)
- Representing Molecular Features: “Molecule models” 山本海行
（MIYUKI YAMAMOTO） / CC BY-SA 4.0 (cropped) - Anomaly Detection in Blockchain Transactions: “EduBlock” BeeBringer / CC0 (cropped)
- Functional Design of Graphene: “Neon atoms between graphene sheets ( )” Oak Ridge National Laboratory / CC BY 2.0 (cropped)
- AI-Based Design of Functional Molecules: “121-70SRibosomes antibiotics” David Goodsell / CC BY 3.0 (cropped)
- Related lab (Category Theory and Formal Methods Lab): “Commutative diagram zelmerszoetrop” Zelmerszoetrop (talk) / CC0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “Biomechanics-Femur-Fracture-Nail-Internal Fixation-CAD-FEM” Fry72 Karel Frydrýšek, Tomáš Halo, Daniel Čepica / CC BY-SA 4.0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “AbsoluteErrorNumericalDifferentiationExample” Berland / Public domain (cropped)
- Related lab (Social Mathematics and Computer Algebra Lab): “Mathics screenshot” Wikideas1 / CC0 (cropped)
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