Related papers: Posterior-First Neural PDE Simulation: Inferring H…

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Deep neural networks employing error back-propagation for learning can suffer from exploding and vanishing gradient problems. Numerous solutions have been proposed such as normalisation techniques or limiting activation functions to linear…

State-of-the-art backpropagation-free learning methods employ local error feedback to direct iterative optimisation via gradient descent. Here, we examine the more restrictive setting where retrograde communication from neuronal outputs is…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

A reflex is a simple closed loop control approach which tries to minimise an error but fails to do so because it will always react too late. An adaptive algorithm can use this error to learn a forward model with the help of predictive cues.…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

Modern simulation-based inference techniques use neural networks to solve inverse problems efficiently. One notable strategy is neural posterior estimation (NPE), wherein a neural network parameterizes a distribution to approximate the…

Neural PDE surrogates are often deployed in data-limited or partially observed regimes where downstream decisions depend on calibrated uncertainty in addition to low prediction error. Existing approaches obtain uncertainty through ensemble…

Unlike ODEs, whose models involve system matrices and whose controllers involve vector or matrix gains, PDE models involve functions in those roles functional coefficients, dependent on the spatial variables, and gain functions dependent on…

Depth estimation is a cornerstone for autonomous driving, yet acquiring per-pixel depth ground truth for supervised learning is challenging. Self-Supervised Surround Depth Estimation (SSSDE) from consecutive images offers an economical…

Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior…

The variational autoencoder (VAE) is a popular combination of deep latent variable model and accompanying variational learning technique. By using a neural inference network to approximate the model's posterior on latent variables, VAEs…

Simulation-Based Inference (SBI) is a promising Bayesian inference framework that alleviates the need for analytic likelihoods to estimate posterior distributions. Recent advances using neural density estimators in SBI algorithms have…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

Computer simulations have proven a valuable tool for understanding complex phenomena across the sciences. However, the utility of simulators for modelling and forecasting purposes is often restricted by low data quality, as well as…

Detached eclipsing binaries (DEBs) enable direct inference of stellar and orbital properties across diverse stellar populations. However, inference typically requires computationally intensive forward modeling and radial velocity (RV)…

End-to-end autonomous driving has emerged as a dominant paradigm, yet its highly entangled black-box models pose significant challenges in terms of interpretability and safety assurance. To improve model transparency and training…

Current open-loop trajectory models struggle in real-world autonomous driving because minor initial deviations often cascade into compounding errors, pushing the agent into out-of-distribution states. While fully differentiable closed-loop…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…