Arief Anbiya | Searcharxiv

arXiv2026

Estimating Time-Dependent COVID-19 Parameters Using Kolmogorov-Arnold Network and Physics-Informed Neural Network

We introduce a novel method for estimating COVID-19 time-varying parameters. These parameters are in the context of an SIRD compartmental differential equations. The time-dependent parameters are the transmission rate $\beta(t)$, recovery rate $\gamma(t)$, and mortality rate $\mu(t)$. The method harnesses the novel Kolmogorov-Arnold Network (KAN), which is a type of artificial neural network. For the KAN in this paper, we learn activation functions that are represented using Fourier series, hence the abbreviation KAN-F. We define three KAN-F functions $\widehat{\beta}$, $\widehat{\gamma}$, $\widehat{\mu}$ that model the true parameters $\beta(t)$, $\gamma(t)$, $\mu(t)$, respectively. We investigate two model architectures for the KAN-F: the first has 8 input variables consisting of $S$, $I$, $R$, $D$, and their numerical gradients at any time $t$, while the second has 4 input variables excluding the numerical gradients. The objective loss function that has to be minimized is subject to Physics-Informed Neural Network (PINN) or Epi-DNN. We estimate the time-dependent parameters of COVID-19 using data from three South-East Asian countries: Indonesia, Singapore, and Malaysia. The time period of choice coincides with the period where SARS-CoV-2 Delta variant (B.1.617.2) was dominant. Using Epi-DNN and KAN-F, we are able to estimate $\beta(t)$, $\gamma(t)$, and $\mu(t)$, with decent accuracy and comparative efficiency. In addition to estimating the rates during the training period, we also predict transmission rates over 30 days during forecasting period. We found that the output of KAN-F over the forecasting period can give good predictions if we scale the output by a factor of 17\% for Indonesia and 30\% for Singapore and Malaysia.

q-bio.OT↗

arXiv2026

Numerical Methods for a 2D "Bad" Boussinesq Equation: RK4, Strang Splitting, and High-frequency Fourier Modes

Numerical methods for a two-dimensional ``bad'' Boussinesq equation: $u_{tt} = u_{xx} + u_{xxxx} + u_{yy} - 3 (u^{2})_{xx}$ are presented with good accuracy. The methods mainly depend on pseudo-spectral Fourier with a trimming of carefully chosen high-frequency Fourier modes. One method also relies on Runge-Kutta fourth order (RK4), and another method relies on Strang operator splitting. Before implementing the two methods, we analyze using Fourier series the linearized version of the equation by removing the nonlinear term $3(u^{2})_{xx}$, and found that a particular bound or condition needs to be satisfied to avoid blow-up solution. We found that high-frequency Fourier modes that do not satisfy the condition must be excluded from the Fourier solution. We then apply this condition to the numerical methods for solving the nonlinear Boussinesq equation and found that including only the Fourier modes that satisfy the condition gives stable numerical solution with good accuracy up to $t=100$. Including even just a few number of Fourier modes that violate the condition can result in a blow-up solution as early as $t=23.5$. The accuracy of the method is measured by computing the $L^{\infty}$ error against a soliton exact solution. The errors resulting from RK4 and Strang splitting numerical simulations differ slightly for small $\triangle t$, while there is a noticeable decrease in performance for the Strang splitting simulation as $\triangle t$ increases. Using our numerical methods, we also display a simulation with Dirichlet boundary condition to account for wave reflections.

physics.flu-dyn↗