Scientific Simulation

Pre-trained machine learning (ML) models have shown great performance for a wide range of applications, in particular in natural language processing (NLP) and computer vision (CV). Here, we study how pre-training could be used for scientific machine learning (SciML) applications, specifically in the context of transfer learning. We study the transfer behavior of these models as (i) the pretrained model size is scaled, (ii) the downstream training dataset size is scaled, (iii) the physics parameters are systematically pushed out of distribution, and (iv) how a single model pre-trained on a mixture of different physics problems can be adapted to various downstream applications. We find that—when fine-tuned appropriately—transfer learning can help reach desired accuracy levels with orders of magnitude fewer downstream examples (across different tasks that can even be out-of-distribution) than training from scratch, with consistent behaviour across a wide range of downstream examples. We also find that fine-tuning these models yields more performance gains as model size increases, compared to training from scratch on new downstream tasks. These results hold for a broad range of PDE learning tasks. All in all, our results demonstrate the potential of the “pre-train and fine-tune” paradigm for SciML problems, demonstrating a path towards building SciML foundation models. Our code is available as open-source.

Spiking Neural Networks (SNNs) are biologically-inspired models that are capable of processing information in streams of action potentials. However, simulating and training SNNs is computationally expensive due to the need to solve large systems of coupled differential equations. In this paper, we propose a novel event-based algorithm called SparseProp for simulating and training sparse SNNs. Our algorithm reduces the computational cost of both forward pass and backward pass operations from O(N) to O(log(N)) per network spike, enabling numerically exact simulations of large spiking networks and their efficient training using backpropagation through time. By exploiting the sparsity of the network, SparseProp avoids iterating through all neurons at every spike and uses efficient state updates. We demonstrate the effectiveness of SparseProp for several classical integrate-and-fire neuron models, including simulating a sparse SNN with one million LIF neurons, which is sped up by more than four orders of magnitude compared to previous implementations. Our work provides an efficient and exact solution for training large-scale spiking neural networks and opens up new possibilities for building more sophisticated brain-inspired models.

Different outdoor illumination conditions drastically alter the appearance of urban scenes, and they can harm the performance of image-based robot perception systems if not seen during training. Camera simulation provides a cost-effective solution to create a large dataset of images captured under different lighting conditions. Towards this goal, we propose LightSim, a neural lighting camera simulation system that enables diverse, realistic, and controllable data generation. LightSim automatically builds lighting-aware digital twins at scale from collected raw sensor data and decomposes the scene into dynamic actors and static background with accurate geometry, appearance, and estimated scene lighting. These digital twins enable actor insertion, modification, removal, and rendering from a new viewpoint, all in a lighting-aware manner. LightSim then combines physically-based and learnable deferred rendering to perform realistic relighting of modified scenes, such as altering the sun location and modifying the shadows or changing the sun brightness, producing spatially- and temporally-consistent camera videos. Our experiments show that LightSim generates more realistic relighting results than prior work. Importantly, training perception models on data generated by LightSim can significantly improve their performance. Our project page is available at https://waabi.ai/lightsim/.

One-shot channel simulation is a fundamental data compression problem concerned with encoding a single sample from a target distribution $Q$ using a coding distribution $P$ using as few bits as possible on average. Algorithms that solve this problem find applications in neural data compression and differential privacy and can serve as a more efficient and natural alternative to quantization-based methods. Unfortunately, existing solutions are too slow or have limited applicability, preventing their widespread adaptation. In this paper, we conclusively solve one-shot channel simulation for one-dimensional problems where the target-proposal density ratio is unimodal by describing an algorithm with optimal runtime. We achieve this by constructing a rejection sampling procedure equivalent to greedily searching over the points of a Poisson process. Hence, we call our algorithm greedy Poisson rejection sampling (GPRS) and analyze the correctness and time complexity of several of its variants. Finally, we empirically verify our theorems, demonstrating that GPRS significantly outperforms the current state-of-the-art method, A* coding.

Simulation-based inference (SBI) enables amortized Bayesian inference for simulators with implicit likelihoods. But when we are primarily interested in the quality of predictive simulations, or when the model cannot exactly reproduce the observed data (i.e., is misspecified), targeting the Bayesian posterior may be overly restrictive. Generalized Bayesian Inference (GBI) aims to robustify inference for (misspecified) simulator models, replacing the likelihood-function with a cost function that evaluates the goodness of parameters relative to data. However, GBI methods generally require running multiple simulations to estimate the cost function at each parameter value during inference, making the approach computationally infeasible for even moderately complex simulators. Here, we propose amortized cost estimation (ACE) for GBI to address this challenge: We train a neural network to approximate the cost function, which we define as the expected distance between simulations produced by a parameter and observed data. The trained network can then be used with MCMC to infer GBI posteriors for any observation without running additional simulations. We show that, on several benchmark tasks, ACE accurately predicts cost and provides predictive simulations that are closer to synthetic observations than other SBI methods, especially for misspecified simulators. Finally, we apply ACE to infer parameters of the Hodgkin-Huxley model given real intracellular recordings from the Allen Cell Types Database. ACE identifies better data-matching parameters while being an order of magnitude more simulation-efficient than a standard SBI method. In summary, ACE combines the strengths of SBI methods and GBI to perform robust and simulation-amortized inference for scientific simulators.

We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original $N$-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an $O(1/\sqrt{N})$ optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require \emph{any} additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.