arXiv subjects

Cassio M. Oishi

Publications and source records attributed to Cassio M. Oishi.

8 recordsLinked to original sources

arXiv2026

Robust Sparse Identification of Nonlinear Dynamics via Least Trimmed Squares

In this work, we propose a robust Sparse Identification of Nonlinear Dynamics (SINDy) pipeline for handling datasets corrupted by noise and outliers. The method decouples outlier filtering from sparse regression by combining Iterative Least Trimmed Squares (ILTS) with Sequentially Thresholded Least Squares (STLS). Unlike standard approaches that treat all observations uniformly within a single regression stage, the proposed ILTS-SINDy framework first applies an ILTS procedure that iteratively minimizes the sum of the smallest squared residuals to identify the most reliable observations without prior knowledge of outliers, after which STLS is used to recover a parsimonious governing model. Extensive numerical experiments show that ILTS-SINDy can significantly outperform existing robust SINDy variants across a range of outlier contamination levels, with performance maintained even under settings with up to $20\%$ corrupted observations.

math.OC↗

arXiv2026

Prediction of Viscoelastic Droplet Impact Dynamics Using a Vision Transformer-Based Approach

Droplet impact on solid surfaces is a complex fluid dynamics problem with applications in spray cooling, inkjet printing, and pharmaceutical processing. Although numerical simulations are widely used to investigate these dynamics, their computational cost becomes significant when multiple parametric variations are considered. In this work, we investigate the use of a Video Vision Transformer (ViViT) architecture to predict the temporal evolution of viscoelastic droplets impacting solid surfaces using volume fraction fields obtained from the Volume of Fluid (VOF) method. In Newtonian fluids, impact dynamics are mainly characterized by the Reynolds number $Re$, representing the ratio of inertial to viscous forces, and the Weber number $We$, representing the ratio of inertial to surface tension forces. For viscoelastic fluids, additional parameters are required to account for elastic effects, namely the solvent viscosity ratio $β$ and the Weissenberg number $Wi$, increasing simulation complexity and cost. Instead of simulating the entire droplet dynamics, the proposed approach uses only the initial 10% to 20% of the simulation to predict the remaining evolution. Depending on the prediction configuration, this strategy reduces computational cost by approximately 80% to 90% compared to full numerical simulations. The ViViT produces physically consistent predictions across different parameters and prediction horizons, successfully capturing both spreading and bouncing regimes while preserving geometric features and structural similarity. Since volume fraction fields can also be extracted from experimental videos, the proposed framework could be extended to incorporate experimental data during training, potentially improving the physical fidelity of the predicted dynamics.

physics.flu-dyn↗

arXiv2025

From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on SINDy-type algorithms. STLS is an algorithm to solve the $\ell_0$ sparse least-squares problem, which relies on splitting to efficiently solve the least-squares portion while handling the sparse term via proximal methods. It produces coefficient vectors whose components depend on both the projected reconstruction errors, here referred to as the scores, and the mutual coherence of dictionary terms. The first contribution of this work is a theoretical analysis of the score and dictionary-selection strategy. This could be understood in both the original and weak SINDy regime. Second, numerical experiments on ordinary and partial differential equations highlight the effectiveness of score-based screening, improving both accuracy and interpretability in dynamical system identification. These results suggest that integrating score-guided methods to refine the dictionary more accurately may help SINDy users in some cases to enhance their robustness for data-driven discovery of governing equations.

stat.ML↗

arXiv2025

Predicting Energy Budgets in Droplet Dynamics: A Recurrent Neural Network Approach

Neural networks in fluid mechanics offer an efficient approach for exploring complex flows, including multiphase and free surface flows. The recurrent neural network, particularly the Long Short-Term Memory (LSTM) model, proves attractive for learning mappings from transient inputs to dynamic outputs. This study applies LSTM to predict transient and static outputs for fluid flows under surface tension effects. Specifically, we explore two distinct droplet dynamic scenarios: droplets with diverse initial shapes impacting with solid surfaces, as well as the coalescence of two droplets following collision. Using only dimensionless numbers and geometric time series data from numerical simulations, LSTM predicts the energy budget. The marker-and-cell front-tracking methodology combined with a marker-and-cell finite-difference strategy is adopted for simulating the droplet dynamics. Using a recurrent neural network (RNN) architecture fed with time series data derived from geometrical parameters, as for example droplet diameter variation, our study shows the accuracy of our approach in predicting energy budgets, as for instance the kinetic, dissipation, and surface energy trends, across a range of Reynolds and Weber numbers in droplet dynamic problems. Finally, a two-phase sequential neural network using only geometric data, which is readily available in experimental settings, is employed to predict the energies and then use them to estimate static parameters, such as the Reynolds and Weber numbers. While our methodology has been primarily validated with simulation data, its adaptability to experimental datasets is a promising avenue for future exploration. We hope that our strategy can be useful for diverse applications, spanning from inkjet printing to combustion engines, where the prediction of energy budgets or dissipation energies is crucial.

physics.flu-dyn↗

arXiv2024

Machine Learning in Viscoelastic Fluids via Energy-Based Kernel Embedding

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce a kernel function corresponding to a given viscoelastic stress model that implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) whose squared norm equals the total mechanical energy. Working implicitly with lifted representations in the RKHS via the kernel function provides natural and unambiguous metrics for distances and angles between flowfields without the need for hyperparameter tuning. Additionally, we present a solution to the preimage problem for our kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of our kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using our kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.

physics.flu-dyn↗

arXiv2023

Nonlinear parametric models of viscoelastic fluid flows

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modeling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics algorithm to develop interpretable reduced-order models for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data is predominantly concentrated on a limit cycle regime for moderate Wi, we show that the parameterized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in the field of reduced-order modeling for viscoelastic flows with the potential to be further refined and enhanced for the design, optimization, and control of a wide range of non-Newtonian fluid flows using machine learning and reduced-order modeling techniques.

physics.flu-dyn↗

arXiv2023

Elasto-viscoplastic Spreading: from Plastocapillarity to Elastocapillarity

We study the spreading of elastoviscoplastic (EVP) droplets under surface tension effects. The non- Newtonian material flows like a viscoelastic liquid above the yield stress and behaves like a viscoelastic solid below it. Hence, the droplet initially flows under surface tension forces but eventually reaches a final equilibrium shape when the stress everywhere inside the droplet falls below the resisting rheological stresses. We use numerical simulations and combine Volume-of-Fluid (VOF) method and an EVP constitutive model to systematically study the dynamics of spreading and the final shape of the droplets. The spreading process examined in this study finds applications in coating, droplet-based inkjet printing, and 3D printing, where complex fluids such as paints, thermoplastic filaments, or bio-inks are deposited onto surfaces. Additionally, the computational framework enables the study of a wide range of multiphase interfacial phenomena, from elastocapillarity to plastocapillarity.

cond-mat.soft↗

arXiv2021

Second-order finite difference approximations of the upper-convected time derivative

In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers.

math.NA↗