Self-Flow-Matching assisted Full Waveform Inversion

arXiv (Cornell University) · 2026-03-13

Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.

Self-Flow-Matching assisted Full Waveform Inversion

ArXiv.org · 2026-03-13

Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.

Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective

ArXiv.org · 2025-02-02 · 7 citations

Multi-task learning through composite loss functions is fundamental to modern deep learning, yet optimizing competing objectives remains challenging. We present new theoretical and practical approaches for addressing directional conflicts between loss terms, demonstrating their effectiveness in physics-informed neural networks (PINNs) where such conflicts are particularly challenging to resolve. Through theoretical analysis, we demonstrate how these conflicts limit first-order methods and show that second-order optimization naturally resolves them through implicit gradient alignment. We prove that SOAP, a recently proposed quasi-Newton method, efficiently approximates the Hessian preconditioner, enabling breakthrough performance in PINNs: state-of-the-art results on 10 challenging PDE benchmarks, including the first successful application to turbulent flows with Reynolds numbers up to 10,000, with 2-10x accuracy improvements over existing methods. We also introduce a novel gradient alignment score that generalizes cosine similarity to multiple gradients, providing a practical tool for analyzing optimization dynamics. Our findings establish frameworks for understanding and resolving gradient conflicts, with broad implications for optimization beyond scientific computing.

A foundation model for the Earth system

Nature · 2025-05-21 · 121 citations

Reliable forecasting of the Earth system is essential for mitigating natural disasters and supporting human progress. Traditional numerical models, although powerful, are extremely computationally expensive1. Recent advances in artificial intelligence (AI) have shown promise in improving both predictive performance and efficiency2,3, yet their potential remains underexplored in many Earth system domains. Here we introduce Aurora, a large-scale foundation model trained on more than one million hours of diverse geophysical data. Aurora outperforms operational forecasts in predicting air quality, ocean waves, tropical cyclone tracks and high-resolution weather, all at orders of magnitude lower computational cost. With the ability to be fine-tuned for diverse applications at modest expense, Aurora represents a notable step towards democratizing accurate and efficient Earth system predictions. These results highlight the transformative potential of AI in environmental forecasting and pave the way for broader accessibility to high-quality climate and weather information. Aurora, a new large-scale foundation model trained on more than one million hours of diverse geophysical data, outperforms operational forecasts in predicting air quality, ocean wave dynamics, tropical cyclone tracks and high-resolution weather.

Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuators

IEEE Robotics and Automation Letters · 2025-09-02 · 1 citations

Soft pneumatic actuators (SPA) made from elastomeric materials can provide large strain and large force. The behavior of locally strain-restricted hyperelastic materials under inflation has been investigated thoroughly for shape reconfiguration, but requires further investigation for trajectories involving external force. In this work we model force-pressure-height relationships for a concentrically strain-limited class of soft pneumatic actuators and demonstrate the use of this model to design SPA response for object lifting. We predict relationships under different loadings by solving energy minimization equations and verify this theory by using an automated test rig to collect rich data for n=22 Ecoflex 00-30 membranes. We collect data using an active learning pipeline to efficiently model the design space. We show that this learned model outperforms the theory-based model and a naive regression. We use our model to optimize membrane design for different lift tasks and compare this performance to other designs. These contributions represent a step towards understanding the natural response for this class of actuator and embodying intelligent lifts in a single-pressure input actuator system.

Reduced order computational fluid dynamic simulations in the thoracic aorta are associated with disease recorded in a medical biobank

Scientific Reports · 2025-11-10

This study examines the association of aortic geometric traits with flow characteristics and disease outcomes in 3204 patients from the Penn Medicine Biobank (PMBB). Using an nnU-Net, the thoracic aorta was segmented from CT scans to measure traits such as diameter and length. A one-dimensional reduced-order Navier-Stokes model (ROM) simulated aortic pulse pressure under various physiological conditions. Phenome-wide association studies (PheWAS) were conducted to link aortic traits to diseases using electronic health records (EHR). Significant associations were identified between aortic pulse pressure and conditions like aortic aneurysms, heart valve disorders, hypertension, and obesity. Notably, pulse pressure-but not aortic diameter-was also linked to diseases such as diabetes mellitus, wheezing, and chronic airway obstruction. The ROM-simulated pulse pressure showed not only previously recognized associations with diseases such as aortic aneurysm and hypertension, but also associations with conditions affecting organs outside the aorta. ROM hemodynamic simulations can be applied to thoracic images at the scale of thousands of patients. The ROM-simulated pulse pressure showed not only previously recognized associations with diseases including aortic aneurysm and hypertension, but also other diseases outside the aorta.

Simulating Three-dimensional Turbulence with Physics-informed Neural Networks

ArXiv.org · 2025-07-11

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically different approach that trains neural networks directly from physical equations rather than data, offering the potential for continuous, mesh-free solutions. Here we show that appropriately designed PINNs can successfully simulate fully turbulent flows in both two and three dimensions, directly learning solutions to the fundamental fluid equations without traditional computational grids or training data. Our approach combines several algorithmic innovations including adaptive network architectures, causal training, and advanced optimization methods to overcome the inherent challenges of learning chaotic dynamics. Through rigorous validation on challenging turbulence problems, we demonstrate that PINNs accurately reproduce key flow statistics including energy spectra, kinetic energy, enstrophy, and Reynolds stresses. Our results demonstrate that neural equation solvers can handle complex chaotic systems, opening new possibilities for continuous turbulence modeling that transcends traditional computational limitations.

Pulmonary Artery Shear Stress and Oscillatory Shear Index are Associated with Right Ventricular Remodeling in Repaired Tetralogy of Fallot

Annals of Biomedical Engineering · 2025-07-03 · 2 citations

Abstract Purpose Right ventricular (RV) remodeling in repaired tetralogy of Fallot (rToF) is a multifactorial process that may be affected by downstream hemodynamics. We therefore sought to characterize hemodynamics in the pulmonary arteries (PAs) of rToF patients using cardiovascular magnetic resonance (CMR)-derived computational fluid dynamics (CFD) and to study these variables in association with RV measurements at follow-up. Methods We selected patients with two CMRs who had magnetic resonance angiography (MRA) performed at baseline. The PA was segmented from the main PA (MPA) through the first bifurcation of the left PA (LPA) and right PA (RPA). Both steady and pulsatile simulations were performed. For each vessel, we calculated curvature, tortuosity, and both average (avg) and peak steady WSS (WSS steady ), time-averaged WSS (taWSS), WSS in systole (WSS systole ), and WSS in diastole (WSS diastole ), as well as oscillatory shear index (OSI). We studied these variables in association with RV metrics at follow-up including: RV end-diastolic volume index (RVEDVi), RV end-systolic volume index (RVESVi), RV stroke volume index (RVSVi), and RV ejection fraction (RVEF), as well as the outcome of pulmonic valve replacement (PVR). Results 22 patients met the inclusion criteria. Several focal hemodynamic metrics in the main and branch PAs, including WSS steady , taWSS, WSS systole , WSS diastole, and OSI were associated with RV measurements at follow-up, including RVEDVi, RVESVi, and RVSVi. LPA WSS steady,avg , RPA WSS steady,peak , whole vessel OSI avg , and MPA OSI avg were associated with likelihood of PVR. Conclusion CFD-derived hemodynamic variables in the PAs of rToF patients are associated with both PVR and RV remodeling.

Abstract 4367228: Asymmetric Pulmonary Artery Geometry Drives Branch-Specific Shear Stress Patterns in Repaired Tetralogy of Fallot: A Substudy of the <i>Single Center Cardiac Magnetic Resonance Outcomes Registry – Tetralogy of Fallot</i>

Circulation · 2025-11-03

Introduction: In repaired tetralogy of Fallot (rToF), asymmetric remodeling of the pulmonary arteries (PA) leads to branch-specific hemodynamic changes. Geometric factors such as curvature influence wall shear stress (WSS) patterns, with distinct effects between the left (LPA) and right pulmonary arteries (RPA). Oscillatory shear index (OSI), which quantifies directional changes in WSS over the cardiac cycle, is a key marker of disturbed flow. This study investigates how curvature and other geometric factors influence hemodynamics in these two branches. Hypothesis: We hypothesize that geometric features influence PA hemodynamics in a branch-specific manner, with curvature having a stronger association with shear-related metrics in certain regions compared to others. Methods: Patient-specific PA models (n = 22) were reconstructed from cardiac magnetic resonance imaging, and computational fluid dynamics simulations were performed under steady and pulsatile flow conditions with patient-derived boundary conditions. Geometric parameters, including curvature and tortuosity, and hemodynamic metrics, including time-averaged WSS and OSI, were quantified. Spearman correlations assessed branch-specific relationships. Results: In the LPA, curvature showed a strong positive correlation with time-averaged WSS (ρ = 0.56, p = 0.006) and a negative correlation with OSI (ρ = -0.52, p = 0.013), indicating that higher curvature segments exhibit more unidirectional, high-shear flow (Figures 1 and 2) . In contrast, RPA curvature did not correlate significantly with any of the measured hemodynamic variables (all p &gt; 0.28). The LPA curvature was significantly greater than the RPA curvature (p = 0.015). Tortuosity did not show significant correlations with hemodynamics in either branch (p &gt; 0.17), suggesting that curvature is the dominant geometric modulator of wall shear stress (Table 1) . Conclusions: The LPA’s curvature-dependent hemodynamics characterized by significant time-averaged WSS and OSI patterns contrast with the RPA’s lack of such correlations. Anatomically, the RPA’s straighter anatomy minimizes flow disruption whereas the LPA curvature increases flow disruption. This study’s results align with prior studies showing sharper angulation in the LPA post-repair, promoting flow acceleration. Clinically, these findings highlight the importance of branch-specific geometric and hemodynamic assessments in rToF follow-up.

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Computer Methods in Applied Mechanics and Engineering · 2025-10-12 · 4 citations