# Estimation of System Parameters Including Repeated Cross-Sectional Data through Emulator-Informed Deep Generative Model

arXiv: https://arxiv.org/abs/2412.19517 · HTML: https://mlsanity.com/paper/2412.19517/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 27 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [GATSBI: Generative Adversarial Training for Simulation-Based Inference](https://mlsanity.com/paper/2203.06481/) (2022)
- [HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork](https://mlsanity.com/paper/2312.15949/) (2023)
- [Deep Neural Network Approach to Forward-Inverse Problems](https://mlsanity.com/paper/1907.12925/) (2019)

## Built on by (most cited first, 1 of 1)

- [Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model](https://mlsanity.com/paper/2507.10884/) (2025)

## Abstract (arXiv)

Differential equations (DEs) are crucial for modeling the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data from system observations. However, in fields such as politics, economics, and biology, available data are often independently collected at distinct time points from different subjects (i.e., repeated cross-sectional (RCS) data). Conventional optimization techniques struggle to accurately estimate DE parameters when RCS data exhibit various heterogeneities, leading to a significant loss of information. To address this issue, we propose a new estimation method called the emulator-informed deep-generative model (EIDGM), designed to handle RCS data. Specifically, EIDGM integrates a physics-informed neural network-based emulator that immediately generates DE solutions and a Wasserstein generative adversarial network-based parameter generator that can effectively mimic the RCS data. We evaluated EIDGM on exponential growth, logistic population models, and the Lorenz system, demonstrating its superior ability to accurately capture parameter distributions. Additionally, we applied EIDGM to an experimental dataset of Amyloid beta 40 and beta 42, successfully capturing diverse parameter distribution shapes. This shows that EIDGM can be applied to model a wide range of systems and extended to uncover the operating principles of systems based on limited data.