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Lecture

AI4Science at Microsoft: Catalyst Design & Material Discovery

In course

ChE-605: AI in chemistry and beyond:Highlights in the field

Should have expertise in chemistry, physics or lite and material sciences. Although a very good knowledge in Al-based algorithms is required to fully understand the technical details, a basic knowledge is sufficient to understand the potential of these met ...

Description

This lecture introduces AI4Science at Microsoft, a team focusing on machine learning, quantum physics, computational chemistry, molecular biology, and fluid dynamics to address societal challenges. The talk delves into accelerating catalyst design through scalable simulation methods, exploring reaction mechanisms, and automating reaction network exploration. It covers challenges in exploring high-dimensional spaces, designing efficient simulation methods, and generative modeling of materials using Clifford algebra. The lecture showcases the application of Clifford convolution and Fourier transform in PDE modeling, with promising results in weather modeling, Maxwell's equations, and shallow water simulations.

Instructor

Philippe Schwaller

Official source

Related concepts (31)

Clifford algebra

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and .

Classification of Clifford algebras

In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras for a nondegenerate quadratic form have been completely classified. In each case, the Clifford algebra is algebra isomorphic to a full matrix ring over R, C, or H (the quaternions), or to a direct sum of two copies of such an algebra, though not in a canonical way.

Clifford module

In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field K over which the quadratic form Q defining C is defined. The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature p − q (mod 8).

Geometric algebra

In mathematics, a geometric algebra (also known as a real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division and addition of objects of different dimensions.

Weyl algebra

In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form More precisely, let F be the underlying field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F[X]. ∂X is the derivative with respect to X. The algebra is generated by X and ∂X. The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring.

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