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Abstract Our recent work on linear and affine dynamical systems has laid out a general framework for inferring the parameters of a differential equation model from a discrete set of data points collected from a system being modeled. It introduced a new class of inverse problems where qualitative information about the parameters and the associated dynamics of the system is determined for regions of the data space, rather than just for isolated experiments. Rigorous mathematical results have justified this approach and have identified common features that arise for certain classes of integrable models. In this work we present a thorough numerical investigation that shows that several of these core features extend to a paradigmatic linear-in-parameters model, the Lotka–Volterra (LV) system, which we consider in the conservative case as well as under the addition of terms that perturb the system away from this regime. A central construct for this analysis is a concise representation of parameter and dynamical features in the data space that we call thePn-diagram, which is particularly useful for visualization of the qualitative dependence of the system dynamics on data for low-dimensional (smalln) systems. Our work also exposes some new properties related to non-uniqueness that arise for these LV systems, with non-uniqueness manifesting as a multi-layered structure in the associatedP2-diagrams.
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Capturing the science behind the craft: a reporting framework to improve quality and confidence in nonsimulated models
Abstract Qualitative nonsimulated models (causal loop diagrams, stock‐flow diagrams, or hybrids of both) have been used since within a decade after the inception of system dynamics (SD). In this article, we assert that the well‐known weaknesses of nonsimulated models need to be balanced against the contexts, purposes, and strengths that nonsimulated models provide. We propose a framework consisting of a set of best practices for model reporting and documentation that would improve the quality, consistency, and transparency of nonsimulated models. Several high‐quality examples are described and referenced in the framework to illustrate support of each criterion. The framework's purpose is help improve the transparency around the creation and evaluation of nonsimulated models, thereby enhancing their confidence and legitimate use in SD practice. Ultimately, high‐quality nonsimulated models can offer broader access to the powerful body of SD knowledge to audiences likely never to have access to formal SD simulation models. © 2023 System Dynamics Society.
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- Award ID(s):
- 1914745
- PAR ID:
- 10473259
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- System Dynamics Review
- Volume:
- 40
- Issue:
- 4
- ISSN:
- 0883-7066
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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