PDE
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Switched Event-Triggered Adaptive Control of Reaction-Diffusion PDE-ODE with Neural Operator Implementation
arXiv:2606.02114v1 Announce Type: cross Abstract: This paper develops a switched event-triggered adaptive boundary control for a class of reaction-diffusion PDE-ODE cascade systems, where the system and input matrices in the ODE as well as the spatially-varying reaction coefficient in the PDE are uncertain. A two-step backstepping transformation is constructed to derive the continuous-time control law. Then a novel dynamic event-triggered control strategy for the PDE-ODE cascade is proposed...
PDE-Agents: An LLM-Orchestrated Multi-Agent Framework for Automated Finite Element Simulations with Knowledge Graph-Augmented Reasoning
Announce Type: new Abstract: We present PDE-Agents, a multi-agent ecosystem that automates the full lifecycle of partial differential equation (PDE) / finite element method (FEM) simulations through natural-language interaction. Three specialist large language model (LLM) agents (Simulation, Analytics, Database) are orchestrated via a LangGraph supervisor, with a local open-source LLM stack (Qwen3-Coder-Next, Llama 4 Scout) on dual NVIDIA RTX PRO 6000 GPUs. The architecture is...
The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems
arXiv:2606.04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution. Conditioning a generative prior on a hard PDE constraint is...
The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems
Announce Type: replace Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution. Conditioning a generative prior on a hard PDE constraint is conditioning on...
The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems
arXiv:2606.04804v3 Announce Type: replace Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution. Conditioning a generative prior on a hard PDE constraint...
A Variational Framework for the Complexity of PDE Solutions
arXiv:2510.21290v3 Announce Type: replace Abstract: Partial Differential Equations (PDEs) are fundamental mathematical models for describing physical phenomena, yet most PDEs of practical interest require numerical approximations. The feasibility of such methods is constrained by existing computational models. Since digital computers are the primary realizations of numerical computations, and Turing machines define their theoretical limits, computability of PDE solutions is of fundamental...
Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
arXiv:2606.02623v1 Announce Type: new Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering. Physics-informed neural networks (PINNs) learn PDE solutions from governing equations. However, accurately capturing temporal evolution remains challenging.
Flowers: A Warp Drive for Neural PDE Solvers
arXiv:2603.04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displacement field and warps the mixed input features.
The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence
arXiv:2606.04018v1 Announce Type: new Abstract: We study neural approximation of elliptic PDE solutions from a variational perspective. The central point is the distinction between the geometry of neural parameters and the convergence of the corresponding physical states. Even when the original elliptic energy is coercive and strictly convex in the natural energy space, its restriction to a nonlinear neural ansatz may fail to be coercive in parameter space.
Multilevel Stochastic Gradient Descent for Risk-Averse PDE-Constrained Optimization
Announce Type: cross Abstract: We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The algorithm uses adaptive multilevel Monte Carlo gradient estimates, provides parallel scalability as well as improved convergence rates and computational complexity compared to standard batched stochastic gradient descent methods. We study the method in computationally demanding...