We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based state-space backbone with an operator-theoretic decoder, enabling scalable and data-efficient modeling of complex physical dynamics. In contrast to task-specific neural operators, PDE-FM is pretrained once on diverse PDE datasets and can be transferred to new physical regimes without architectural or data-specific modifications. Evaluated on twelve 2D and 3D datasets from The Well benchmark - spanning hydrodynamic, radiative, elastic, and astrophysical phenomena - PDE-FM achieves state-of-the-art accuracy in six domains, reducing mean VRMSE by 46% relative to prior operator-learning baselines. The model demonstrates robust cross-physics generalization, excelling in turbulent and radiative systems while maintaining strong performance in linear and steady-state regimes. These results suggest that large-scale pretraining across diverse physical processes can yield transferable representations of dynamics, marking a step toward unified, foundation-level surrogates for multi-physics simulation and scientific discovery.

Neural Information Processing Systems http://nips.cc/

In recent years, automated mechanism design has emerged as one of the most practical and promising approaches to designing high-revenue combinatorial auctions.

Magnetic levitation is about to revolutionize in-machine material flow in industrial automation. Such systems are flexibly configurable and can include a large number of independently actuated shuttles (movers) that dynamically rebalance production capacity. Beyond their capabilities for dynamic transportation, these systems possess the inherent yet unexploited potential to perform manipulation. By merging the fields of transportation and manipulation into a coordinated swarm of magnetic robots (MagBots), we enable manufacturing systems to achieve significantly higher efficiency, adaptability, and compactness. To support the development of intelligent algorithms for magnetic levitation systems, we introduce MagBotSim (Magnetic Robotics Simulation): a physics-based simulation for magnetic levitation systems. By framing magnetic levitation systems as robot swarms and providing a dedicated simulation, this work lays the foundation for next generation manufacturing systems powered by Magnetic Robotics. MagBotSim's documentation, videos, experiments, and code are available at: https://ubi-coro.github.io/MagBotSim/

There is growing interest in combining model-free and model-based approaches in reinforcement learning with the goal of achieving the high performance of model-free algorithms with low sample complexity. This is difficult because an imperfect dynamics model can degrade the performance of the learning algorithm, and in sufficiently complex environments, the dynamics model will always be imperfect. As a result, a key challenge is to combine model-based approaches with model-free learning in such a way that errors in the model do not degrade performance. We propose stochastic ensemble value expansion (STEVE), a novel model-based technique that addresses this issue. By dynamically interpolating between model rollouts of various horizon lengths, STEVE ensures that the model is only utilized when doing so does not introduce significant errors. Our approach outperforms model-free baselines on challenging continuous control benchmarks with an order-of-magnitude increase in sample efficiency.

In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed neural networks (PINNs), these weights are often adaptively chosen to improve the network's generalization error. A popular choice of adaptive weights is based on the neural tangent kernel (NTK) of the PINN, which describes the evolution of the network in predictor space during training. The convergence of such an adaptive weighting algorithm is not clear a priori. Moreover, these NTK-based weights would be updated frequently during training, further increasing the computational burden of the learning process. In this paper, we prove that under appropriate conditions, gradient descent enhanced with adaptive NTK-based weights is convergent in a suitable sense. We then address the problem of computational efficiency by developing a randomized algorithm inspired by a predictor-corrector approach and matrix sketching, which produces unbiased estimates of the NTK up to an arbitrarily small discretization error. Finally, we provide numerical experiments to support our theoretical findings and to show the efficacy of our randomized algorithm. Code Availability: https://github.com/maxhirsch/Efficient-NTK

This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix.

Training neural operators to approximate mappings between infinite-dimensional function spaces often requires extensive datasets generated by either demanding experimental setups or computationally expensive numerical solvers. This dependence on solver-based data limits scalability and constrains exploration across physical systems. Here we introduce the Method of Manufactured Learning (MML), a solver-independent framework for training neural operators using analytically constructed, physics-consistent datasets. Inspired by the classical method of manufactured solutions, MML replaces numerical data generation with functional synthesis, i.e., smooth candidate solutions are sampled from controlled analytical spaces, and the corresponding forcing fields are derived by direct application of the governing differential operators. During inference, setting these forcing terms to zero restores the original governing equations, allowing the trained neural operator to emulate the true solution operator of the system. The framework is agnostic to network architecture and can be integrated with any operator learning paradigm. In this paper, we employ Fourier neural operator as a representative example. Across canonical benchmarks including heat, advection, Burgers, and diffusion-reaction equations. MML achieves high spectral accuracy, low residual errors, and strong generalization to unseen conditions. By reframing data generation as a process of analytical synthesis, MML offers a scalable, solver-agnostic pathway toward constructing physically grounded neural operators that retain fidelity to governing laws without reliance on expensive numerical simulations or costly experimental data for training.

We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic differentiation (AD) enables direct gradient-based estimation of complex boundary admittance from sparse pressure measurements, achieving 3-digit precision without requiring manual derivation of adjoint equations. Second, we apply randomized finite differences to acoustic shape optimization, combining JAX-FEM for forward simulation with PyTorch3D for mesh manipulation through AD. By separating physics-driven boundary optimization from geometry-driven interior mesh adaptation, we achieve 48.1% energy reduction at target frequencies with 30-fold fewer FEM solutions compared to standard finite difference on the full mesh. This work showcases how modern differentiable software stacks enable rapid prototyping of optimization workflows for physics-based inverse problems, with automatic differentiation for parameter estimation and a combination of finite differences and AD for geometric design.