A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to train approximations to multiple differential equations simultaneously and are thus a general purpose solver that can be adapted to downstream tasks. Current PDE foundation models focus on either learning general solution operators and/or the governing system of equations, and thus only handle numerical or symbolic modalities. However, real-world applications may require more flexible data modalities, e.g. text analysis or descriptive outputs. To address this gap, we propose a novel multimodal deep learning approach that leverages a transformer-based architecture to approximate solution operators for a wide variety of ODEs and PDEs. Our method integrates numerical inputs, such as equation parameters and initial conditions, with text descriptions of physical processes or system dynamics. This enables our model to handle settings where symbolic representations may be incomplete or unavailable. In addition to providing accurate numerical predictions, our approach generates interpretable scientific text descriptions, offering deeper insights into the underlying dynamics and solution properties. The numerical experiments show that our model provides accurate solutions for in-distribution data (with average relative error less than 3.3%) and out-of-distribution data (average relative error less than 7.8%) together with precise text descriptions (with correct descriptions generated 100% of times). In certain tests, the model is also shown to be capable of extrapolating solutions in time.

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics

We introduce BCAT, a PDE foundation model designed for autoregressive prediction of solutions to two dimensional fluid dynamics problems. Our approach uses a block causal transformer architecture to model next frame predictions, leveraging previous frames as contextual priors rather than relying solely on sub-frames or pixel-based inputs commonly used in image generation methods. This block causal framework more effectively captures the spatial dependencies inherent in nonlinear spatiotemporal dynamics and physical phenomena. In an ablation study, next frame prediction demonstrated a 2.9x accuracy improvement over next token prediction. BCAT is trained on a diverse range of fluid dynamics datasets, including incompressible and compressible Navier-Stokes equations across various geometries and parameter regimes, as well as the shallow-water equations. The model's performance was evaluated on 6 distinct downstream prediction tasks and tested on about 8K trajectories to measure robustness on a variety of fluid dynamics simulations. BCAT achieved an average relative error of 1.92% across all evaluation tasks, outperforming prior approaches on standard benchmarks.

Automatically Planning Optimal Parallel Strategy for Large Language Models

The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for parallel computing is becoming increasingly important. In this paper, we propose an automatic parallel algorithm that automatically plans the parallel strategy with maximum throughput based on model and hardware information. By decoupling the training time into computation, communication, and overlap, we established a training duration simulation model. Based on this simulation model, we prune the parallel solution space to shorten the search time required. The multi-node experiment results show that the algorithm can estimate the parallel training duration in real time with an average accuracy of 96%. In our test, the recommendation strategy provided by the algorithm is always globally optimal.

DeepSeek-V3 Technical Report

We present DeepSeek-V3, a strong Mixture-of-Experts (MoE) language model with 671B total parameters with 37B activated for each token. To achieve efficient inference and cost-effective training, DeepSeek-V3 adopts Multi-head Latent Attention (MLA) and DeepSeekMoE architectures, which were thoroughly validated in DeepSeek-V2. Furthermore, DeepSeek-V3 pioneers an auxiliary-loss-free strategy for load balancing and sets a multi-token prediction training objective for stronger performance. We pre-train DeepSeek-V3 on 14.8 trillion diverse and high-quality tokens, followed by Supervised Fine-Tuning and Reinforcement Learning stages to fully harness its capabilities. Comprehensive evaluations reveal that DeepSeek-V3 outperforms other open-source models and achieves performance comparable to leading closed-source models. Despite its excellent performance, DeepSeek-V3 requires only 2.788M H800 GPU hours for its full training. In addition, its training process is remarkably stable. Throughout the entire training process, we did not experience any irrecoverable loss spikes or perform any rollbacks. The model checkpoints are available at https://github.com/deepseek-ai/DeepSeek-V3.

VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction

In-Context Operator Networks (ICONs) are models that learn operators across different types of PDEs using a few-shot, in-context approach. Although they show successful generalization to various PDEs, existing methods treat each data point as a single token, and suffer from computational inefficiency when processing dense data, limiting their application in higher spatial dimensions. In this work, we propose Vision In-Context Operator Networks (VICON), incorporating a vision transformer architecture that efficiently processes 2D functions through patch-wise operations. We evaluated our method on three fluid dynamics datasets, demonstrating both superior performance (reducing scaled $L^2$ error by $40\%$ and $61.6\%$ for two benchmark datasets for compressible flows, respectively) and computational efficiency (requiring only one-third of the inference time per frame) in long-term rollout predictions compared to the current state-of-the-art sequence-to-sequence model with fixed timestep prediction: Multiple Physics Pretraining (MPP). Compared to MPP, our method preserves the benefits of in-context operator learning, enabling flexible context formation when dealing with insufficient frame counts or varying timestep values.

Synth4Seg -- Learning Defect Data Synthesis for Defect Segmentation using Bi-level Optimization

Defect segmentation is crucial for quality control in advanced manufacturing, yet data scarcity poses challenges for state-of-the-art supervised deep learning. Synthetic defect data generation is a popular approach for mitigating data challenges. However, many current methods simply generate defects following a fixed set of rules, which may not directly relate to downstream task performance. This can lead to suboptimal performance and may even hinder the downstream task. To solve this problem, we leverage a novel bi-level optimization-based synthetic defect data generation framework. We use an online synthetic defect generation module grounded in the commonly-used Cut\&Paste framework, and adopt an efficient gradient-based optimization algorithm to solve the bi-level optimization problem. We achieve simultaneous training of the defect segmentation network, and learn various parameters of the data synthesis module by maximizing the validation performance of the trained defect segmentation network. Our experimental results on benchmark datasets under limited data settings show that the proposed bi-level optimization method can be used for learning the most effective locations for pasting synthetic defects thereby improving the segmentation performance by up to 18.3\% when compared to pasting defects at random locations. We also demonstrate up to 2.6\% performance gain by learning the importance weights for different augmentation-specific defect data sources when compared to giving equal importance to all the data sources.

Cerberus: Efficient Inference with Adaptive Parallel Decoding and Sequential Knowledge Enhancement

Large language models (LLMs) often face a bottleneck in inference speed due to their reliance on auto-regressive decoding. Recently, parallel decoding has shown significant promise in enhancing inference efficiency. However, we have identified two key issues with existing parallel decoding frameworks: (1) decoding heads fail to balance prediction accuracy and the parallelism of execution, and (2) parallel decoding is not a universal solution, as it can bring unnecessary overheads at some challenging decoding steps. To address these issues, we propose Cerberus, an adaptive parallel decoding framework introduces the gating mechanism to enable the LLMs to adaptively choose appropriate decoding approaches at each decoding step, along with introducing a new paradigm of decoding heads that introduce the sequential knowledge while maintaining execution parallelism. The experiment results demonstrate that the Cerberus can achieve up to 2.12x speed up compared to auto-regressive decoding, and outperforms one of the leading parallel decoding frameworks, Medusa, with a 10% - 30% increase in acceleration and superior generation quality.

Annotation-Free Curb Detection Leveraging Altitude Difference Image

Road curbs are considered as one of the crucial and ubiquitous traffic features, which are essential for ensuring the safety of autonomous vehicles. Current methods for detecting curbs primarily rely on camera imagery or LiDAR point clouds. Image-based methods are vulnerable to fluctuations in lighting conditions and exhibit poor robustness, while methods based on point clouds circumvent the issues associated with lighting variations. However, it is the typical case that significant processing delays are encountered due to the voluminous amount of 3D points contained in each frame of the point cloud data. Furthermore, the inherently unstructured characteristics of point clouds poses challenges for integrating the latest deep learning advancements into point cloud data applications. To address these issues, this work proposes an annotation-free curb detection method leveraging Altitude Difference Image (ADI), which effectively mitigates the aforementioned challenges. Given that methods based on deep learning generally demand extensive, manually annotated datasets, which are both expensive and labor-intensive to create, we present an Automatic Curb Annotator (ACA) module. This module utilizes a deterministic curb detection algorithm to automatically generate a vast quantity of training data. Consequently, it facilitates the training of the curb detection model without necessitating any manual annotation of data. Finally, by incorporating a post-processing module, we manage to achieve state-of-the-art results on the KITTI 3D curb dataset with considerably reduced processing delays compared to existing methods, which underscores the effectiveness of our approach in curb detection tasks.

Depth from Coupled Optical Differentiation

We propose depth from coupled optical differentiation, a low-computation passive-lighting 3D sensing mechanism. It is based on our discovery that per-pixel object distance can be rigorously determined by a coupled pair of optical derivatives of a defocused image using a simple, closed-form relationship. Unlike previous depth-from-defocus (DfD) methods that leverage spatial derivatives of the image to estimate scene depths, the proposed mechanism's use of only optical derivatives makes it significantly more robust to noise. Furthermore, unlike many previous DfD algorithms with requirements on aperture code, this relationship is proved to be universal to a broad range of aperture codes. We build the first 3D sensor based on depth from coupled optical differentiation. Its optical assembly includes a deformable lens and a motorized iris, which enables dynamic adjustments to the optical power and aperture radius. The sensor captures two pairs of images: one pair with a differential change of optical power and the other with a differential change of aperture scale. From the four images, a depth and confidence map can be generated with only 36 floating point operations per output pixel (FLOPOP), more than ten times lower than the previous lowest passive-lighting depth sensing solution to our knowledge. Additionally, the depth map generated by the proposed sensor demonstrates more than twice the working range of previous DfD methods while using significantly lower computation.

PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.