Week 43 · Norm-optimal model order reduction in reproducing kernel Hilbert spaces
Week 43 Physics AI Digest — 10 papers on physics-informed learning, neural operators and surrogate modelling.
Highlights
- This week: 10 papers, focusing on pde, physics-informed, partial differential equation
- Recommendation reasons are auto-generated from paper abstracts; see each entry for details
In this issue
Norm-optimal model order reduction in reproducing kernel Hilbert spaces
We consider the problem of model order reduction (MOR) in reproducing kernel Hilbert spaces (RKHSs). We prove generalizations of well-known necessary interpolatory conditions for norm-optimal reduced-
Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs
Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not su
Synthetic Dataset Generation, Physical Consistency and Active Learning for Shape-Informed Surrogate Modeling of Hemodynamics
Model order reduction has the potential to enable real-time patient-specific assessment of cardiovascular flows. However, it still faces significant challenges stemming from the geometric variability
A mixed leading variable physics-informed neural network for nonsmooth dynamics simulation in contact systems
High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed t
PINN-LPCDD: Physics-Informed Neural Network with Learnable and Physically Consistent Domain Decomposition for Compressible Multi-Medium Flows
The physics-informed neural network (PINN) faces significant challenges when solving compressible multi-medium flows, including the inability to locate interface positions, poor approximation of disco
Learnable Splines for Unstructured Neural Operators
Neural operators approximate solution operators of partial differential equations at a fraction of the cost of numerical solvers. Efficient grid-based architectures such as the Fourier neural operator
Online reduced-order modeling from primal solver trajectories for PDE-constrained optimization
Repeated high-fidelity state and gradient evaluations make large-scale PDE-constrained optimization computationally expensive. Reduced-order modeling provides a natural way to reduce the cost of these
SBNO : Schrödinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information
Partial differential equation (PDE) surrogate modeling often relies on either dense observations or access to governing equations/physics constraints. In practice, observations can be sparse and parti
SINO: Scale-Invariant Neural Operator
In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solving equations on coarse grids, missing information
PI-NOMT: Physics-Informed Neural Optimal Mass Transport for Brain Fluid Dynamics
Recovering hidden transport mechanisms from sparse spatiotemporal observations is a fundamental inverse problem in scientific machine learning. In brain tracer imaging, dynamic contrast-enhanced MRI (
Overview
Week 43 Physics AI Digest — 10 papers on physics-informed learning, neural operators and surrogate modelling.
1. Norm-optimal model order reduction in reproducing kernel Hilbert spaces
We consider the problem of model order reduction (MOR) in reproducing kernel Hilbert spaces (RKHSs). We prove generalizations of well-known necessary interpolatory conditions for norm-optimal reduced-
2. Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs
Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not su
3. Synthetic Dataset Generation, Physical Consistency and Active Learning for Shape-Informed Surrogate Modeling of Hemodynamics
Model order reduction has the potential to enable real-time patient-specific assessment of cardiovascular flows. However, it still faces significant challenges stemming from the geometric variability
4. A mixed leading variable physics-informed neural network for nonsmooth dynamics simulation in contact systems
High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed t
5. PINN-LPCDD: Physics-Informed Neural Network with Learnable and Physically Consistent Domain Decomposition for Compressible Multi-Medium Flows
The physics-informed neural network (PINN) faces significant challenges when solving compressible multi-medium flows, including the inability to locate interface positions, poor approximation of disco
6. Learnable Splines for Unstructured Neural Operators
Neural operators approximate solution operators of partial differential equations at a fraction of the cost of numerical solvers. Efficient grid-based architectures such as the Fourier neural operator
7. Online reduced-order modeling from primal solver trajectories for PDE-constrained optimization
Repeated high-fidelity state and gradient evaluations make large-scale PDE-constrained optimization computationally expensive. Reduced-order modeling provides a natural way to reduce the cost of these
8. SBNO : Schrödinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information
Partial differential equation (PDE) surrogate modeling often relies on either dense observations or access to governing equations/physics constraints. In practice, observations can be sparse and parti
9. SINO: Scale-Invariant Neural Operator
In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solving equations on coarse grids, missing information
10. PI-NOMT: Physics-Informed Neural Optimal Mass Transport for Brain Fluid Dynamics
Recovering hidden transport mechanisms from sparse spatiotemporal observations is a fundamental inverse problem in scientific machine learning. In brain tracer imaging, dynamic contrast-enhanced MRI (