Steven Smith: Say It With Matrices? 07-27, 12:00–12:30 (US/Eastern), 32-141
Join us for ASE-60, where we celebrate the life and the career of Professor Alan Stuart Edelman, on the occasion of his 60th birthday: https://math.mit.edu/events/ase60celebration/
My career and contributions have been greatly influenced by Alan Edelman’s work on random matrices, optimization, scientific computing, along with his cherished collaboration and advice. This talk starts with a brief survey of how Alan and his ideas provide a strong foundation for applied research in important areas: random matrices and optimization are applied extensively in diverse fields from sensor arrays to social media networks. The recent, interwoven developments of networked multimedia content sharing and neural-network-based large language and diffusion models would appear to provide a natural home for this theory, which has a great deal to say about the underlying matrices and algorithms that describe both the data and nonlinear optimization methods used in AI. Yet progress in these AI fields has evolved rapidly and spectacularly almost wholly without explicit insights from matrix theory, in spite of their deep reliance on random matrices. The second part of the talk uses related experience from recent work on MCMC- and LLM-based causal inference of real-world network influence to describe the challenges and potential opportunities of applying matrix theory to these recent developments.
Surrogatizing Dynamic Systems using JuliaSim: An introduction. 07-27, 14:00–14:30 (US/Eastern), 32-D463 (Star)
In this talk, we will discuss the use of surrogates in scientific simulations, and introduce JuliaSim, a commercial offering built on top of the SciML ecosystem, and introduce some of the surrogates available in JuliaSim.
In recent years, the use of surrogates in scientific simulations has become increasingly of interest. Surrogates, also known as digital-twins, are approximate models that are trained to mimic the output of a computationally expensive or complex simulation. They can be used to quickly explore the parameter space of a simulation, tune a controller, or optimize inputs and parameters.
The SciML ecosystem is an open-source project that aims to provide a suite of software tools for scientific modeling in the Julia programming language. It includes a wide range of modeling and simulation tools, including differential equations solvers, optimization algorithms, and surrogate models. The goal of SciML is to make it easy for scientists and engineers to use advanced modeling techniques in their work.
JuliaSim is a commercial offering built on top of the open-source SciML ecosystem. It provides a suite of tools for building and deploying surrogate models in Julia. JuliaSim makes it easy to interface with existing simulation codes and dynamic models and also to train, validate, and deploy surrogates using a wide range of algorithms.
In this talk, we will discuss the use of surrogates in scientific simulations, and introduce JuliaSim and discuss the variety of surrogates available in JuliaSim, including their individual specialties.
Sharan Yalburgi
Sharan is a Research Engineer at JuliaHub working on JuliaSim - a modern SciML powered suite for modeling and simulation.
SciML provides tools for a wide problem space. It can be confusing for new users to decide between the packages and the kind of questions that can be answered using each of them. This talk will walk through various ecosystem components for tasks such as inverse problems, model augmentation, and equation discovery and showcase workflows for using these packages with examples based on real-world data.
SciML provides tooling for various Scientific Machine Learning tasks, including parameter estimation, model augmentation, equation discovery, ML-based solvers for differential equations, and surrogatization. It can be confusing for new users to reason about the various packages, including DiffEqParamEstim, DiffEqFlux, DataDrivenDiffEq, NeuralPDE, and Surrogates etc., and their suitability for the problem they want to solve. We plan to provide a wide overview of the SciML ecosystem packages, describing the kinds of questions that each of these packages is suitable to answer. Additionally, we will demonstrate sample SciML workflows that show the composability of the ecosystem.
Vaibhav Dixit
Vaibhav is a Software Engineer at JuliaHub where he works on the Pumas Engineering team. He is an active member of the SciML ecosystem with contributions across parameter estimation and global sensitivity. Utkarsh
Graduate student @ MIT Torkel
Torkel is a Postdoc at the Julia Lab at MIT. His research is on methods for modelling chemical reaction networks, specialising in how these are affected by noise. Torkel
Torkel is a postdoc at the JuliaLab at MIT. His research is on methods for modelling (bio)chemical reaction networks, focusing especially on noise. He is a developer of the Catalyst.jl package.
Geometric Algebra at compile-time with SymbolicGA.jl 07-27, 15:00–15:30 (US/Eastern), 32-144
Geometric Algebra is a high-level mathematical framework which expresses a variety of geometric computations with an intuitive language. While its rich structure unlocks deeper insight and an elegant simplicity, it often comes at a cost to numerical implementations. After giving an overview of geometric algebra and its applications, a Julia implementation is presented which uses metaprogramming to shift the work to compile-time, enabling a fast and expressive approach to computational geometry.
Geometric Algebra is a high-level mathematical framework which expresses a large range of geometric computations in a simple and intuitive language. From a single set of rules and axioms, this framework allows you to create diverse and geometrically meaningful spaces which best suit your needs.
Complex numbers and quaternions may be identified as elements in such spaces which describe rotations in two and three dimensions. These spaces may express Euclidean transformations, such as reflections, rotations and translations; others express intersections of flat geometry such as lines and planes, and may include rounded geometry such as circles and spheres in slightly more complex spaces - all in a dimension-agnostic manner.
The price to pay for this unifying, high-level framework is extra mathematical structure that is generally not a zero-cost abstraction. However, by shifting the application of this structure to compile-time, it is possible to combine the expressive power of geometric algebra with highly performant code.
In this talk, pragmatic motivations for considering geometric algebra are provided, with a quick introduction to its formalism. Then, the open-source SymbolicGA.jl package is presented as a compile-time implementation of geometric algebra. It will be shown that the language of geometric algebra can be used to describe many geometric operations, all with a low symbolic complexity and in a performant manner.
Cédric Belmant
Cédric Belmant is an applied mathematician and programmer, with a strong interest in 3D graphics, geometry processing and application development. He believes the expressive power of the Julia programming language is key to building applications and tools with minimal complexity, and has been exploring ways to integrate computer graphics in the Julia ecosystem. This speaker also appears in:
When type instability matters Towards developing a production app with Julia
SimpleGA. A lightweight Geometric Algebra library. 07-27, 15:30–16:00 (US/Eastern), 32-144
Geometric algebra (GA) is a powerful language for formulating and solving problems in geometry, physics, engineering and graphics. SimpleGA is designed as a straightforward implementation of the most useful geometric algebras, with the key focus on performance. In this talk we use the library to explain some key properties of GA, and explain the motivation behind the design and how it utilises Julia's unique features.
Geometric algebra is a powerful mathematical language that unites many disparate concepts including complex numbers, quaternions, exterior algebra, spinors and projective geometry. The goal with this talk is to use a simple implementation of the algebra to explain the main features. No prior knowledge of geometric (aka Clifford) algebra will be assumed and by the end the audience should have a basic understanding of the properties of the geometric product - the key basis for the algebra. A novel implementation of this product in terms of binary operations will also be discussed. All of the SimpleGA source code is available, and there are many excellent free resources on geometric algebra for those interested in diving deaeper.
Chris Doran
Chris Doran spent the early part of his career researching applications of geometric algebra in quantum theory and gravitation, before switching to graphics. In 2005 he founded Geomerics, which provided real-time global illumination technology to the games industry. Geomerics' Enlighten was used in 100s of games including Dragon Age, Overwatch and Final Fantasy. Chris spent 4 years as a Director of Research at Arm, and now focuses on helping start-ups and university spin-outs. He is currently a Director of Monumo, who are actively using Julia in their research pipeline.
Sound Synthesis with Julia 07-27, 15:30–15:40 (US/Eastern), 32-123
We describe and demonstrate a method to use Julia to generate music on a computer. While electronic music generation has had a long and distinguished history, the use of the Julia programming language provides benefits that are not available using traditional tools in this area.
Most electronic music synthesis software today is written in C/C++. This is usually due to the performance requirements that are necessary in this domain. The use of Julia however brings two distinct advantages to this area.
First, using a high level, dynamic programming language, allows for a wider and more productive range of experimentation. The use of Julia allows for the performance characteristics to me met, while working in an easy to use language. Second, the wide range of high quality mathematical libraries in Julia, from FFT to differential equation solvers, allows for the use of high level constructs, further increasing the productivity of the artist.
In this talk, we show a set of fundamental building blocks for music synthesis in Julia. From wave generators to filters to amplifiers, we will see how these can be built with simple Julia functions, leveraging the existing ecosystem. We will show that Julia's ability to build abstractions without sacrificing performance is crucial to this use case.
Ahan Sengupta
I am a high school student interested in the intersection of programming and music. Avik Sengupta
Avik Sengupta is the head of product development and software engineering at Julia Computing, contributor to open source Julia and maintainer of several Julia packages. Avik is the author of Julia High Performance, co-founder of two artificial intelligence start-ups in the financial services sector and creator of large complex trading systems for the world's leading investment banks.
Keynote: Stephen Wolfram 07-27, 16:15–17:00 (US/Eastern), 26-100
Dr. Stephen Wolfram is the creator of Mathematica, Wolfram|Alpha and the Wolfram Language; the author of A New Kind of Science; the originator of the Wolfram Physics Project; and the founder and CEO of Wolfram Research.
Over the course of more than four decades, he has been a pioneer in the development and application of computational thinking—and has been responsible for many discoveries, inventions and innovations in science, technology and business. Based on both his practical and theoretical thinking, Dr. Wolfram has emerged as an authority on the implications of computation and artificial intelligence for society and the future, and the importance of computational language as a bridge between the capabilities of computation and human objectives.
Dr. Wolfram has been president and CEO of Wolfram Research since its founding in 1987. In addition to his corporate leadership, Wolfram is deeply involved in the development of the company's technology, personally overseeing the functional design of the company's core products on a daily basis, and constantly introducing new ideas and directions.
no subject
https://pretalx.com/juliacon2023/talk/HPT87A/ (not live-streamed/recorded)
The Special Math of Translating Theory To Software in DiffEq
07-27, 11:00–11:30 (US/Eastern), 32-141
Chris Rackauckas: The Special Math of Translating Theory To Software in Differential Equations
The Special Math of Translating Theory To Software in Differential Equations by Chris Rackauckas in 32-141
https://pretalx.com/juliacon2023/talk/3MMRYJ/ (not live-streamed/recorded)
Steven Smith: Say It With Matrices?
07-27, 12:00–12:30 (US/Eastern), 32-141
Join us for ASE-60, where we celebrate the life and the career of Professor Alan Stuart Edelman, on the occasion of his 60th birthday: https://math.mit.edu/events/ase60celebration/
My career and contributions have been greatly influenced by Alan Edelman’s work on random matrices, optimization, scientific computing, along with his cherished collaboration and advice. This talk starts with a brief survey of how Alan and his ideas provide a strong foundation for applied research in important areas: random matrices and optimization are applied extensively in diverse fields from sensor arrays to social media networks. The recent, interwoven developments of networked multimedia content sharing and neural-network-based large language and diffusion models would appear to provide a natural home for this theory, which has a great deal to say about the underlying matrices and algorithms that describe both the data and nonlinear optimization methods used in AI. Yet progress in these AI fields has evolved rapidly and spectacularly almost wholly without explicit insights from matrix theory, in spite of their deep reliance on random matrices. The second part of the talk uses related experience from recent work on MCMC- and LLM-based causal inference of real-world network influence to describe the challenges and potential opportunities of applying matrix theory to these recent developments.
https://pretalx.com/juliacon2023/talk/NLJFAX/
Surrogatizing Dynamic Systems using JuliaSim: An introduction.
07-27, 14:00–14:30 (US/Eastern), 32-D463 (Star)
In this talk, we will discuss the use of surrogates in scientific simulations, and introduce JuliaSim, a commercial offering built on top of the SciML ecosystem, and introduce some of the surrogates available in JuliaSim.
In recent years, the use of surrogates in scientific simulations has become increasingly of interest. Surrogates, also known as digital-twins, are approximate models that are trained to mimic the output of a computationally expensive or complex simulation. They can be used to quickly explore the parameter space of a simulation, tune a controller, or optimize inputs and parameters.
The SciML ecosystem is an open-source project that aims to provide a suite of software tools for scientific modeling in the Julia programming language. It includes a wide range of modeling and simulation tools, including differential equations solvers, optimization algorithms, and surrogate models. The goal of SciML is to make it easy for scientists and engineers to use advanced modeling techniques in their work.
JuliaSim is a commercial offering built on top of the open-source SciML ecosystem. It provides a suite of tools for building and deploying surrogate models in Julia. JuliaSim makes it easy to interface with existing simulation codes and dynamic models and also to train, validate, and deploy surrogates using a wide range of algorithms.
In this talk, we will discuss the use of surrogates in scientific simulations, and introduce JuliaSim and discuss the variety of surrogates available in JuliaSim, including their individual specialties.
Sharan Yalburgi
Sharan is a Research Engineer at JuliaHub working on JuliaSim - a modern SciML powered suite for modeling and simulation.
https://pretalx.com/juliacon2023/talk/MS7SVG/
SciML: Novel Scientific Discoveries through composability
07-27, 14:30–15:00 (US/Eastern), 32-D463 (Star)
SciML provides tools for a wide problem space. It can be confusing for new users to decide between the packages and the kind of questions that can be answered using each of them. This talk will walk through various ecosystem components for tasks such as inverse problems, model augmentation, and equation discovery and showcase workflows for using these packages with examples based on real-world data.
SciML provides tooling for various Scientific Machine Learning tasks, including parameter estimation, model augmentation, equation discovery, ML-based solvers for differential equations, and surrogatization. It can be confusing for new users to reason about the various packages, including DiffEqParamEstim, DiffEqFlux, DataDrivenDiffEq, NeuralPDE, and Surrogates etc., and their suitability for the problem they want to solve. We plan to provide a wide overview of the SciML ecosystem packages, describing the kinds of questions that each of these packages is suitable to answer. Additionally, we will demonstrate sample SciML workflows that show the composability of the ecosystem.
Vaibhav Dixit
Vaibhav is a Software Engineer at JuliaHub where he works on the Pumas Engineering team. He is an active member of the SciML ecosystem with contributions across parameter estimation and global sensitivity.
Utkarsh
Graduate student @ MIT
Torkel
Torkel is a Postdoc at the Julia Lab at MIT. His research is on methods for modelling chemical reaction networks, specialising in how these are affected by noise.
Torkel
Torkel is a postdoc at the JuliaLab at MIT. His research is on methods for modelling (bio)chemical reaction networks, focusing especially on noise. He is a developer of the Catalyst.jl package.
https://pretalx.com/juliacon2023/talk/KPXNR7/
Geometric Algebra at compile-time with SymbolicGA.jl
07-27, 15:00–15:30 (US/Eastern), 32-144
Geometric Algebra is a high-level mathematical framework which expresses a variety of geometric computations with an intuitive language. While its rich structure unlocks deeper insight and an elegant simplicity, it often comes at a cost to numerical implementations. After giving an overview of geometric algebra and its applications, a Julia implementation is presented which uses metaprogramming to shift the work to compile-time, enabling a fast and expressive approach to computational geometry.
Geometric Algebra is a high-level mathematical framework which expresses a large range of geometric computations in a simple and intuitive language. From a single set of rules and axioms, this framework allows you to create diverse and geometrically meaningful spaces which best suit your needs.
Complex numbers and quaternions may be identified as elements in such spaces which describe rotations in two and three dimensions. These spaces may express Euclidean transformations, such as reflections, rotations and translations; others express intersections of flat geometry such as lines and planes, and may include rounded geometry such as circles and spheres in slightly more complex spaces - all in a dimension-agnostic manner.
The price to pay for this unifying, high-level framework is extra mathematical structure that is generally not a zero-cost abstraction. However, by shifting the application of this structure to compile-time, it is possible to combine the expressive power of geometric algebra with highly performant code.
In this talk, pragmatic motivations for considering geometric algebra are provided, with a quick introduction to its formalism. Then, the open-source SymbolicGA.jl package is presented as a compile-time implementation of geometric algebra. It will be shown that the language of geometric algebra can be used to describe many geometric operations, all with a low symbolic complexity and in a performant manner.
Cédric Belmant
Cédric Belmant is an applied mathematician and programmer, with a strong interest in 3D graphics, geometry processing and application development. He believes the expressive power of the Julia programming language is key to building applications and tools with minimal complexity, and has been exploring ways to integrate computer graphics in the Julia ecosystem.
This speaker also appears in:
When type instability matters
Towards developing a production app with Julia
https://pretalx.com/juliacon2023/talk/PK9C77/
SimpleGA. A lightweight Geometric Algebra library.
07-27, 15:30–16:00 (US/Eastern), 32-144
Geometric algebra (GA) is a powerful language for formulating and solving problems in geometry, physics, engineering and graphics. SimpleGA is designed as a straightforward implementation of the most useful geometric algebras, with the key focus on performance. In this talk we use the library to explain some key properties of GA, and explain the motivation behind the design and how it utilises Julia's unique features.
Geometric algebra is a powerful mathematical language that unites many disparate concepts including complex numbers, quaternions, exterior algebra, spinors and projective geometry. The goal with this talk is to use a simple implementation of the algebra to explain the main features. No prior knowledge of geometric (aka Clifford) algebra will be assumed and by the end the audience should have a basic understanding of the properties of the geometric product - the key basis for the algebra. A novel implementation of this product in terms of binary operations will also be discussed. All of the SimpleGA source code is available, and there are many excellent free resources on geometric algebra for those interested in diving deaeper.
Chris Doran
Chris Doran spent the early part of his career researching applications of geometric algebra in quantum theory and gravitation, before switching to graphics. In 2005 he founded Geomerics, which provided real-time global illumination technology to the games industry. Geomerics' Enlighten was used in 100s of games including Dragon Age, Overwatch and Final Fantasy. Chris spent 4 years as a Director of Research at Arm, and now focuses on helping start-ups and university spin-outs. He is currently a Director of Monumo, who are actively using Julia in their research pipeline.
https://pretalx.com/juliacon2023/talk/PYJVRU/
Sound Synthesis with Julia
07-27, 15:30–15:40 (US/Eastern), 32-123
We describe and demonstrate a method to use Julia to generate music on a computer. While electronic music generation has had a long and distinguished history, the use of the Julia programming language provides benefits that are not available using traditional tools in this area.
Most electronic music synthesis software today is written in C/C++. This is usually due to the performance requirements that are necessary in this domain. The use of Julia however brings two distinct advantages to this area.
First, using a high level, dynamic programming language, allows for a wider and more productive range of experimentation. The use of Julia allows for the performance characteristics to me met, while working in an easy to use language. Second, the wide range of high quality mathematical libraries in Julia, from FFT to differential equation solvers, allows for the use of high level constructs, further increasing the productivity of the artist.
In this talk, we show a set of fundamental building blocks for music synthesis in Julia. From wave generators to filters to amplifiers, we will see how these can be built with simple Julia functions, leveraging the existing ecosystem. We will show that Julia's ability to build abstractions without sacrificing performance is crucial to this use case.
Ahan Sengupta
I am a high school student interested in the intersection of programming and music.
Avik Sengupta
Avik Sengupta is the head of product development and software engineering at Julia Computing, contributor to open source Julia and maintainer of several Julia packages. Avik is the author of Julia High Performance, co-founder of two artificial intelligence start-ups in the financial services sector and creator of large complex trading systems for the world's leading investment banks.
https://pretalx.com/juliacon2023/talk/VJRZDF/
Keynote: Stephen Wolfram
07-27, 16:15–17:00 (US/Eastern), 26-100
Dr. Stephen Wolfram is the creator of Mathematica, Wolfram|Alpha and the Wolfram Language; the author of A New Kind of Science; the originator of the Wolfram Physics Project; and the founder and CEO of Wolfram Research.
Over the course of more than four decades, he has been a pioneer in the development and application of computational thinking—and has been responsible for many discoveries, inventions and innovations in science, technology and business. Based on both his practical and theoretical thinking, Dr. Wolfram has emerged as an authority on the implications of computation and artificial intelligence for society and the future, and the importance of computational language as a bridge between the capabilities of computation and human objectives.
Dr. Wolfram has been president and CEO of Wolfram Research since its founding in 1987. In addition to his corporate leadership, Wolfram is deeply involved in the development of the company's technology, personally overseeing the functional design of the company's core products on a daily basis, and constantly introducing new ideas and directions.