A5101961582- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Model Reduction and Neural Networks
- Probabilistic and Robust Engineering Design
- Meteorological Phenomena and Simulations
- Neural Networks and Applications
- Navier-Stokes equation solutions
- Gas Dynamics and Kinetic Theory
- Advanced Numerical Methods in Computational Mathematics
- Geophysics and Gravity Measurements
- Welding Techniques and Residual Stresses
- Wind and Air Flow Studies
- Gaussian Processes and Bayesian Inference
- Numerical Methods and Algorithms
- Numerical methods in inverse problems
- Magnetic Properties and Applications
- Solar and Space Plasma Dynamics
- Microstructure and Mechanical Properties of Steels
- Groundwater flow and contamination studies
- Nuclear reactor physics and engineering
- Hydraulic Fracturing and Reservoir Analysis
- Reservoir Engineering and Simulation Methods
- Seismic Imaging and Inversion Techniques
- Stochastic processes and financial applications
- Ionosphere and magnetosphere dynamics
ETH Zurich
2016-2025
Teerthanker Mahaveer University
2023
Schlumberger (British Virgin Islands)
2019-2022
Tata Institute of Fundamental Research
2021
Applied Mathematics (United States)
2021
University of Oslo
2009-2018
Indian Institute of Information Technology Allahabad
2015
University of Bari Aldo Moro
2013
Board of the Swiss Federal Institutes of Technology
2012
Indian Institute of Technology Bombay
2006-2012
We design arbitrarily high-order accurate entropy stable schemes for systems of conservation laws. The schemes, termed TeCNO are based on two main ingredients: (i) conservative fluxes and (ii) suitable numerical diffusion operators involving ENO reconstructed cell-interface values scaled variables. Numerical experiments in one space dimensions presented to illustrate the robust performance schemes.
Physics-informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems partial differential equations (PDEs). We focus on a particular class of problems, the so-called data assimilation or unique continuation and prove rigorous estimates generalization error PINNs them. An abstract framework is presented conditional stability underlying problem are employed to derive estimate PINN error, providing justification use in this...
Abstract DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze and prove estimates on the resulting approximation generalization errors. In particular, we extend universal property of to include measurable mappings in non-compact By decomposition error into encoding, reconstruction errors, both lower upper bounds total error, relating it spectral decay properties covariance operators, associated...
Abstract We prove rigorous bounds on the errors resulting from approximation of incompressible Navier–Stokes equations with (extended) physics-informed neural networks. show that underlying partial differential equation residual can be made arbitrarily small for tanh networks two hidden layers. Moreover, total error estimated in terms training error, network size and number quadrature points. The theory is illustrated numerical experiments.
We propose a method for solving differential equations.• Our combines PINNs with multilevel domain decomposition.• approach significantly outperforms when multiscale problems.• Multilevel modeling improves accuracy by aiding communication between subdomains.
Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when if such accurately describe the physical observables. Here, we relate these different to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time Bohmian time, are compatible attoclock observable resonance lifetime of bound state, respectively. Both closely connected theory weak measurement, being measurement value tunneling...
We propose a novel machine learning algorithm for simulating radiative transfer. Our is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of underlying tranfer equations. present extensive experiments and theoretical error estimates to demonstrate that PINNs provide very easy implement, fast, robust accurate method also PINN inverse problems transfer efficiently.
We derive bounds on the error, in high-order Sobolev norms, incurred approximation of Sobolev-regular as well analytic functions by neural networks with hyperbolic tangent activation function. These provide explicit estimates error respect to size networks. show that tanh only two hidden layers suffice approximate at comparable or better rates than much deeper ReLU
A standard paradigm for the existence of solutions in fluid dynamics is based on construction sequences approximate or minimizers. This approach faces serious obstacles, most notably multi-dimensional problems, where persistence oscillations at ever finer scales prevents compactness. Indeed, these are an indication, consistent with recent theoretical results, possible lack existence/uniqueness within framework integrable functions. It this context that Young measures – parametrized...
Abstract Physics-informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of partial differential equations (PDEs). We provide upper bounds on the generalization error PINNs approximating solutions forward problem PDEs. An abstract formalism is introduced stability properties underlying PDE are leveraged to derive an estimate in terms training number samples. This framework illustrated with several examples nonlinear Numerical experiments,...
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning that map between infinite-dimensional spaces. We prove FNOs are universal, in the sense they can approximate any continuous operator to desired accuracy. Moreover, we suggest a mechanism by which associated with PDEs efficiently. Explicit error bounds derived show size of FNO, approximating Darcy type elliptic PDE and incompressible Navier-Stokes equations fluid dynamics, only increases sub...
Abstract Physics-informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred PINNs in approximating a large class linear parabolic PDEs, namely Kolmogorov equations that include heat equation and Black-Scholes option pricing, as examples. construct networks, whose PINN residual (generalization error) can be made small desired. also prove total L 2 -error bounded generalization which turn is terms training provided...
We explore the potential of deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within unified variational framework phase-field modeling brittle fracture.We elucidate challenges related neural-network-based approximation energy landscape, ability an optimization approach reach correct minimum, we discuss choices in construction training neural network which prove be critical accurately efficiently...
The automated discovery of constitutive laws forms an emerging research area, that focuses on automatically obtaining symbolic expressions describing the behavior solid materials from experimental data.Existing symbolic/sparse regression methods rely availability libraries material models, which are typically hand-designed by a human expert using known models as reference, or deploy generative algorithms with exponential complexity only practicable for very simple expressions.In this paper,...
Abstract Earth’s spin axis slowly moves relative to the crust over time. A 120-year-long record of this polar motion from astronomical and more modern geodetic measurements displays interannual multidecadal fluctuations 20 40 milliarcseconds superimposed on a secular trend about 3 per year. is thought be driven by various surface interior processes, but how these processes operate interact produce observed signal remains enigmatic. Here we show that predictions made an ensemble...
The melting of ice sheets and global glaciers results in sea-level rise, a pole-to-equator mass transport increasing Earth’s oblateness resulting an increase the length day (LOD). Here, we use observations reconstructions variations at surface since 1900 to show that climate-induced LOD trend hovered between 0.3 1.0 ms/cy 20th century, but has accelerated 1.33 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>±</mml:mo> </mml:math> 0.03...
We deal with a single conservation law in one space dimension whose flux function is discontinuous the variable and we introduce proper framework of entropy solutions. consider large class fluxes, namely, fluxes convex-convex type concave-convex (mixed) type. The alternative that proposed here based on two step approach. In first step, infinitely many classes solutions are defined, each associated an interface connection. show these form contractive semigroup L 1 hence unique. Godunov...