arXiv subjects

Arnav Gangal

Publications and source records attributed to Arnav Gangal.

2 recordsLinked to original sources

arXiv2024

Quantifying the Causal Effect of Financial Literacy Courses on Financial Health

In this study, we investigate the causal effect of financial literacy education on a composite financial health score constructed from 17 self-reported financial health and distress metrics ranging from spending habits to confidence in ability to repay debt to day-to-day financial skill. Leveraging data from the 2021 National Financial Capability Study, we find a significant and positive average treatment effect of financial literacy education on financial health. To test the robustness of this effect, we utilize a variety of causal estimators (Generalized Lin's estimator, 1:1 propensity matching, IPW, and AIPW) and conduct sensitivity analysis using alternate health outcome scoring and varying caliper strengths. Our results are robust to these changes. The robust positive effect of financial literacy education on financial health found here motivates financial education for all individuals and holds implications for policymakers seeking to address the worsening debt problem in the U.S, though the relatively small magnitude of effect demands further research by experts in the domain of financial health.

stat.AP↗

arXiv2023

Physics informed neural networks for elliptic equations with oscillatory differential operators

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to solve equations with multiscale features. The objective of the present work is to illustrate and explain the difficulty of using standard PINNs for the particular case of divergence-form elliptic partial differential equations (PDEs) with oscillatory coefficients present in the differential operator. We show that if the coefficient in the elliptic operator $a^ε(x)$ is of the form $a(x/ε)$ for a 1-periodic coercive function $a(\cdot)$, then the Frobenius norm of the neural tangent kernel (NTK) matrix associated to the loss function grows as $1/ε^2$. This implies that as the separation of scales in the problem increases, training the neural network with gradient descent based methods to achieve an accurate approximation of the solution to the PDE becomes increasingly difficult. Numerical examples illustrate the stiffness of the optimization problem.

math.NA↗