
## Project Overview

This overarching project of many published journal articles addresses key challenges in sampling complex biological (and generically dynamical) systems. We integrated physics-based simulations with machine learning, particularly leveraging generative models to improve molecular phase space sampling (again, as well as sampling of dynamical systems generically) by generating initial conditions that are consistent with specific values of pertinent collective variables (CVs) of the system of interest. 

If these CVs were not known already, we identify them with manifold learning. We also show that enhanced sampling methods can be used directly with CVs in embedding (lower dimensional manifold) space. The manifold learning method used in these works to get to that lower dimensional embedding space are diffusion maps (and geometric harmonics to get from embedding space back to the ambient space). Additionally, we developed generative modeling frameworks that combine diffusion models and manifold learning to efficiently sample complex data distributions. 

I continued this work in the context of materials discovery for NASA’s Biological and Physical Sciences division, establishing a novel AI framework for generating alloy compositions with target properties Utilizing a framework that can be thought of as a VAE wrapper around a Diffusion model. 

The articles that comprise this work are shortly and informally described below. Please give some of them a further read if the summaries interest you.

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## GANs and Closures

The seminal work in this project, this study explores how combining physics-based simulation methods with machine learning techniques, like conditional generative adversarial networks (cGANs), can enhance sampling in complex molecular systems by generating realistic high-dimensional states from simpler low-dimensional representations. The approach leverages known system characteristics or learns important features using tools like diffusion maps, using them to bias the generated states to specific regions in collective variable (CV) space. This is also the paper that shows you can bias enhanced sampling methods directly with embedded CVs. You do not have to bias in the physical/ambient space of the system!

[View details and external link to paper](../research/gans-closures)

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## Micro-macro consistency in multiscale modeling: Score-based model assisted sampling of fast/slow dynamical systems

The second work extends the work of GANs and Closures to new classes of generative models, i.e. score-based diffusion models (abbreviated here as SGMs). This study explores how combining physics-based enhanced sampling techniques with machine learning tools like SGMs can help tackle the challenges of efficiently sampling multiscale dynamical systems.

[View details and external link to paper](../research/micro-macro)

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## Generative Learning for Slow Manifolds and Bifurcation Diagrams

This paper proposes a framework leveraging conditional score-based generative models (cSGMs) and nonlinear dimensionality reduction techniques to efficiently approximate slow manifolds and construct bifurcation diagrams in multiscale dynamical systems. The approach circumvents fast transient dynamics and identifies steady states by directly initializing on the low-dimensional slow manifold of a system.

[View details and external link to paper](../research/gen-bifurcations)

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## Generative Learning of Densities on Manifolds

This study introduces and validates a framework for generating data distributions on high-dimensional manifolds using modified score-based generative models (m-SGMs). The model leverages nonlinear dimensionality reduction methods to address challenges in high-dimensional uncertainty quantification. Applications in computational mechanics demonstrate the robustness and efficiency of the proposed approach over conventional methods.

[View details and external link to paper](../research/gen-densities)

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## Inverse Design of Alloys via Generative Algorithms: Optimization and Diffusion within Learned Latent Space

Using the same principals for a NASA and materials science adjacent problem, this study introduces a generative AI framework using variational autoencoders (VAEs) and SGMs as inverse design methods to efficiently discover new alloy compositions with desired properties, tackling challenges like limited data, solution nonuniqueness, and complex design spaces. By enabling smooth mapping of properties and generating diverse compositions, the approach shows promise for accelerating the identification of desired alloy compositions.

[View details and external link to paper](../research/inverse-alloys)


A collection of papers demonstrating that generative model architectures (such as GANs and diffusion models) can efficiently sample and explore the phase space of various dynamical systems including molecular conformational space described by collective variables (that are found with diffusion maps or known beforehand), bifurcation diagrams, low dimensional manifolds of high dimensional systems, and more.

Generative Model Assisted Sampling of Dynamical Systems


## Project Overview

This collection of papers as a project explores the use of ionic polyimides (i-PIs) as advanced materials for CO2 capture and gas separation, leveraging molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations to understand and optimize their adsorption and diffusion properties. The addition of imidazolium-based ionic liquids (ILs) greatly enhances gas separation performance by lowering the i-PI glass transition temperature (Tg), improving CO2 solubility, and creating favorable transport pathways at higher IL concentrations. Investigations into various IL anions, such as [Tf2N−], [PF6−], [BF4−], [oAc−], and [C(CN)3−], reveal their distinct effects on adsorption properties, solubility, and diffusivity, with [C(CN)3−]-based systems showing particularly improved CO2 diffusion. Surface area, fractional free volume, and polymer relaxation were revealed as critical structural factors linked to adsorption behavior, while IL inclusion significantly alters molecular-level interactions, enhancing selectivity for CO2 over CH4 and N2. This comprehensive study provides valuable insights into designing and optimizing i-PIs and i-PI + IL composites for high-performance gas separation membranes.

The articles that comprise this work are shortly and informally described below. Please give some of them a further read if the summaries interest you.

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## Molecular Simulation of Ionic Polyimides and Composites with Ionic Liquids as Gas-Separation Membranes

This study investigates CO2 and CH4 adsorption in ionic polyimides (i-PIs) and i-PI + ionic liquid (IL) composites using molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations. Results reveal that surface area plays a critical role in gas solubility during polymer relaxation and that the presence of IL alters molecular adsorption sites, improving selectivity in gas purification processes.

[View details and external link to paper](../research/molecular-simulation)

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## Molecular analysis of selective gas adsorption within composites of ionic polyimides and ionic liquids as gas separation membranes

The second work of this project models the CO2 separation performance of ionic polyimides (i-PIs) and their composites with various ionic liquids (ILs) using molecular dynamics and Monte Carlo simulations. Results show that IL inclusion enhances gas selectivity, with [PF6−]-based composites improving CO2/CH4 selectivity by 36%, while [Tf2N−]-based systems exhibit higher CO2/N2 selectivity, driven by differences in structural properties like fractional free volume and surface area.

[View details and external link to paper](../research/molecular-analysis)

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## Molecular Transport Behavior of CO2 in Ionic Polyimides and Ionic Liquid Composite Membrane Materials

This third publication combines Monte Carlo and molecular dynamics simulations to explore the equilibrium and transport properties of CO2 in ionic polyimides (i-PIs) and i-PI + ionic liquid (IL) composites, revealing that IL addition lowers the glass transition temperature (Tg) of i-PIs, enhancing CO2 solubility. While low IL concentrations hinder diffusion via a blocking effect, higher IL concentrations facilitate transport by increasing polymer plasticization and creating favorable pathways for CO2 movement.

[View details and external link to paper](../research/molecular-transport)

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## Solubility and diffusivity of CO2 in ionic polyimides with [C(CN)3]x[oAc]1−x anion composition

This study uses molecular dynamics and Monte Carlo simulations to investigate the adsorption and diffusion properties of CO2 in ionic polyimides (i-PIs) with acetate ([oAc−]) and tricyanomethanide ([C(CN)3−]) anions, revealing that higher [C(CN)3−] concentrations enhance CO2 diffusion while maintaining solubility. Structural analyses show diffusivity correlates moderately with fractional free volume (FFV), providing insight into how anion composition impacts performance in i-PI gas separation membranes, distinct from pure ionic liquid behavior.

[View details and external link to paper](../research/solubility)



A collection of papers involving the atomistic and molecular behavior of ionic polyimides as gas separation membranes. Ionic liquids were also used as solvents to situationally improve adsorption performance.

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Generative Model Assisted Sampling of Dynamical Systems

Molecular Simulation and Analysis of Ionic Polyimide Membranes in Ionic Liquid Solvents