Large Science Models (LSM):

Collaborative Acceleration Via Digital Twins

Ishanu Chattopadhyay, PhD

Assistant Professor

University of Chicago

ishanu@uchicago.edu

Large Science Models (LSMs)

  • LLMs have revolutionized how we think about using and manipulating the human language. Likewise LSMs could transform the scientific field, with AI begining to understand hard science concepts, theories and data, and reason with complex mathematical models, much in analogy to how AI "understands" the human language in "large language models".

Digital Twins (Teomims) of Complex Systems:

  • LSMs would lead to the emergence of digital twins  of complex natural  systems, and help us explore the hypothesis spaces which currently can only be sampled serendipitously. Thus we might evolve beyond guessing hypotheses ,  and embark on a principled exploration of such spaces

Expanding the Scientific Method:  

  • AI collaboration can finally allow us to find "complex" explanations, exploring that part of nature which cannot be written down on a postage stamp

Nicholas Sizemore et al. ,A digital twin of the infant microbiome to predict neurodevelopmental deficits.Sci. Adv.10,eadj0400(2024).DOI:10.1126/sciadv.adj0400

G_{\mu\nu}+\Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}

Assuming  a 1000 species ecosystem, and 1 successful experiment every day to discern a single two-way relationship, we would need 1,368 years to go through all possibilities. If we look for 3 way interactions, we would need 454,844 years

E=MC\(^2\)

ih\frac{\partial \psi}{\partial t} = \hat{H} \psi

Complex systems have irreducible complexity.

Generative models of complex systems must have complex structure, which can be only recovered vi AI-leveraged methods

Large Science Models (LSM):

The Quasinet Framework

\textrm{Let } X_1, \cdots, X_N \textrm{ take values in } \Sigma_i\\\Phi \triangleq\left \{ \Phi_i: \prod_{j \neq i}\mathcal{D}_{j} \rightarrow \mathcal{D}_i, i \in N\right \} \\ \textrm{ where } \mathcal{D}_i \textrm{ is a probability measure over set } \Sigma_i
  • \(N\) is large
  • Each \(\Phi_i\) is a conditional inference tree
  • \(\Sigma_i\) are finite but possibly non-identical
\theta(x,y) = \mathbf{E}_i [ J^{\frac{1}{2}}(\Phi_i(x_{-i}),\Phi_i(y_{-i})) ]

The intrinsic distance:

A view of a Complex Systems as  Interacting Q-fields

\textrm{ Let } \psi(x,t) \in \textrm{ be random variable at time } t \\\textrm{ taking values in } \bigotimes_i \Sigma_i
\mathcal{L} = T -V = \psi \nabla^2 \psi - \psi\vert \vert\phi
\Delta_i \psi(x_1, ..., x_i, ..., x_n) = \\\frac{1}{2} \left ( \psi(x_1, ..., x_i + 1, ..., x_n) - 2\psi(x_1, ..., x_i, ..., x_n) + \psi(x_1, ..., x_i - 1, ..., x_n) \right )
KE(\psi) = \sum_{i=1}^n \sum_{x_1 \in S_1} \cdots \sum_{x_n \in S_n} \psi(x_1, ..., x_n) \Delta_i \psi(x_1, ..., x_n)
\mathcal{L} = T -V = \psi \nabla^2 \psi - \psi\vert \vert\phi
\Delta_i \psi(x_1, ..., x_i, ..., x_n) = \\\frac{1}{2} \left ( \psi(x_1, ..., x_i + 1, ..., x_n) - 2\psi(x_1, ..., x_i, ..., x_n) + \psi(x_1, ..., x_i - 1, ..., x_n) \right )
KE(\psi) = \sum_{i=1}^n \sum_{x_1 \in S_1} \cdots \sum_{x_n \in S_n} \psi(x_1, ..., x_n) \Delta_i \psi(x_1, ..., x_n)
\textrm{Euler-Lagrance or Klein-Gordon Eqn.}\\\textrm{yields the Eqns of motion:}\\ \frac{\partial \mathcal{L}}{\partial \psi} - \partial_\mu \left(\frac{\partial \mathcal{L}}{\partial (\partial_\mu \psi)}\right) = 0

This requires us to specify the Lagrangian

Large Science Models (LSM):

Collaborative Acceleration Via Digital Twins

Large Science Models (LSMs)

  • LLMs have revolutionized how we think about using and manipulating the human language. Likewise LSMs could transform the scientific field, with AI begining to understand hard science concepts, theories and data, and reason with complex mathematical models, much in analogy to how AI "understands" the human language in "large language models".

Digital Twins (Teomims) of Complex Systems:

  • LSMs would lead to the emergence of digital twins  of complex natural  systems, and help us explore the hypothesis spaces which currently can only be sampled serendipitously. Thus we might evolve beyond guessing hypotheses ,  and embark on a principled exploration of such spaces

Expanding the Scientific Method:  

  • AI collaboration can finally allow us to find "complex" explanations, exploring that part of nature which cannot be written down on a postage stamp

Nicholas Sizemore et al. ,A digital twin of the infant microbiome to predict neurodevelopmental deficits.Sci. Adv.10,eadj0400(2024).DOI:10.1126/sciadv.adj0400

Assuming  a 1000 species ecosystem, and 1 successful experiment every day to discern a single two-way relationship, we would need 1,368 years to go through all possibilities. If we look for 3 way interactions, we would need 454,844 years

Complex systems have irreducible complexity.

Generative models of complex systems must have complex structure, which can be only recovered vi AI-leveraged methods

Complementary AI Workshop

By Ishanu Chattopadhyay

Complementary AI Workshop

Predictive modeling of crime and rare phenomena using fractal nets

  • 159

More from Ishanu Chattopadhyay