arXiv subjects

Michal Balcerak

Publications and source records attributed to Michal Balcerak.

11 recordsLinked to original sources

arXiv2026

An Imaging-Informed Reaction-Diffusion Model of Infarct Growth

Predicting final ischemic infarct volumes from acute imaging is a cornerstone of personalized stroke management, yet current strategies remain polarized between uninterpretable machine learning architectures and overly detailed electrophysiological models that are intractable in clinical imaging settings. We bridge this clinical gap by introducing the first imaging-driven framework that parameterizes a Fisher-KPP reaction-diffusion partial differential equation (PDE) directly from clinical acute MRI. The continuous state variable $u(\mathbf{x},t)\in[0,1]$ models tissue damage, capturing the forward expansion of ionic stress through the extracellular space alongside a localized metabolic commitment to cell death gated within the baseline perfusion deficit ($T_{\max}>6$\,s). Evaluating this paradigm on a subset of the ISLES 2017 dataset ($N=29$) via an oracle framework reveals that incorporating biophysical propagation constraints yields a mean Dice score of $0.46 \pm 0.24$, compared to standard rCBF thresholding ($0.25 \pm 0.21$). Extensive ablations demonstrate that modeling spatially heterogeneous diffusion fields derived from clinical perfusion maps accurately captures penumbral expansion, while providing full physiological interpretability. This proof-of-concept establishes that first-principles physics could capture complex ischemic progression directly on clinical scan grids, shifting the paradigm from purely data-driven models toward patient-specific biophysical forecasting.

cs.CE↗

arXiv2026

Projected Energy Matching for Generative 3D Priors

Energy Matching has emerged as a powerful generative framework that combines flow model efficiency with the explicit likelihood of Energy-Based Models (EBMs) via a single, time-independent scalar potential. However, directly training this potential on high-dimensional 3D data remains computationally challenging. While distilling a pre-trained flow model circumvents some of the initial training costs, we demonstrate that velocity fields inevitably contain non-conservative rotational artifacts (curl). Forcing a strictly conservative scalar potential to match this unconstrained field creates a "structural conflict", which degrades generation quality and mode coverage. To solve this, we propose Projected Energy Matching, a scalable framework that resolves these structural and computational bottlenecks. We introduce Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network. We subsequently refine this landscape using Negative Caching, a memory-efficient strategy that reuses negative samples across micro-batches, rendering sampling tractable during contrastive training with gradient accumulation. We deploy our method as an unconditional prior for real-world medical CT inverse problems, specifically sparse-view reconstruction. Ultimately, our amortized pipeline reduces total compute to a small fraction of that required by standard energy matching, while achieving high-fidelity reconstructions and successfully resolving severe measurement artifacts.

eess.IV↗

arXiv2026

Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation

Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan-Kinderlehrer-Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs. Project page: https://michalbalcerak.ai/graph-energy-matching/.

cs.LG↗

arXiv2025

From Fiber Tracts to Tumor Spread: Biophysical Modeling of Butterfly Glioma Growth Using Diffusion Tensor Imaging

Butterfly tumors are a distinct class of gliomas that span the corpus callosum, producing a characteristic butterfly-shaped appearance on MRI. The distinctive growth pattern of these tumors highlights how white matter fibers and structural connectivity influence brain tumor cell migration. To investigate this relation, we applied biophysical tumor growth models to a large patient cohort, systematically comparing models that incorporate fiber tract information with those that do not. Our results demonstrate that including fiber orientation data significantly improves model accuracy, particularly for a subset of butterfly tumors. These findings highlight the critical role of white matter architecture in tumor spread and suggest that integrating fiber tract information can enhance the precision of radiotherapy target volume delineation.

physics.med-ph↗

arXiv2025

Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In contrast, energy-based models (EBMs) address this by incorporating corresponding scalar energy terms. Here, we propose Energy Matching, a framework that endows flow-based approaches with the flexibility of EBMs. Far from the data manifold, samples move from noise to data along irrotational, optimal transport paths. As they approach the data manifold, an entropic energy term guides the system into a Boltzmann equilibrium distribution, explicitly capturing the underlying likelihood structure of the data. We parameterize these dynamics with a single time-independent scalar field, which serves as both a powerful generator and a flexible prior for effective regularization of inverse problems. The present method substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation in terms of fidelity, while retaining simulation-free training of transport-based approaches away from the data manifold. Furthermore, we leverage the flexibility of the method to introduce an interaction energy that supports the exploration of diverse modes, which we demonstrate in a controlled protein generation setting. This approach learns a scalar potential energy, without time conditioning, auxiliary generators, or additional networks, marking a significant departure from recent EBM methods. We believe this simplified yet rigorous formulation significantly advances EBMs capabilities and paves the way for their wider adoption in generative modeling in diverse domains.

cs.LG↗

arXiv2024

A Lightweight Optimization Framework for Estimating 3D Brain Tumor Infiltration

Glioblastoma, the most aggressive primary brain tumor, poses a severe clinical challenge due to its diffuse microscopic infiltration, which remains largely undetected on standard MRI. As a result, current radiotherapy planning employs a uniform 15 mm margin around the resection cavity, failing to capture patient-specific tumor spread. Tumor growth modeling offers a promising approach to reveal this hidden infiltration. However, methods based on partial differential equations or physics-informed neural networks tend to be computationally intensive or overly constrained, limiting their clinical adaptability to individual patients. In this work, we propose a lightweight, rapid, and robust optimization framework that estimates the 3D tumor concentration by fitting it to MRI tumor segmentations while enforcing a smooth concentration landscape. This approach achieves superior tumor recurrence prediction on 192 brain tumor patients across two public datasets, outperforming state-of-the-art baselines while reducing runtime from 30 minutes to less than one minute. Furthermore, we demonstrate the framework's versatility and adaptability by showing its ability to seamlessly integrate additional imaging modalities or physical constraints.

physics.med-ph↗

arXiv2024

Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient's anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

cs.CV↗

arXiv2024

A Learnable Prior Improves Inverse Tumor Growth Modeling

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%.

physics.med-ph↗

arXiv2023

Individualizing Glioma Radiotherapy Planning by Optimization of Data and Physics-Informed Discrete Loss

Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss, where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation model, which is adapted for complex cases.

physics.med-ph↗

arXiv2023

Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion PDE model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse domain method is employed to handle the complex brain geometry within the PINN framework. Our method is validated both on synthetic and patient datasets, and shows promise for real-time parametric inference in the clinical setting for personalized GBM treatment.

cs.LG↗

arXiv2020

Constructing trading strategy ensembles by classifying market states

Rather than directly predicting future prices or returns, we follow a more recent trend in asset management and classify the state of a market based on labels. We use numerous standard labels and even construct our own ones. The labels rely on future data to be calculated, and can be used a target for training a market state classifier using an appropriate set of market features, e.g. moving averages. The construction of those features relies on their label separation power. Only a set of reasonable distinct features can approximate the labels. For each label we use a specific neural network to classify the state using the market features from our feature space. Each classifier gives a probability to buy or to sell and combining all their recommendations (here only done in a linear way) results in what we call a trading strategy. There are many such strategies and some of them are somewhat dubious and misleading. We construct our own metric based on past returns but penalising for a low number of transactions or small capital involvement. Only top score-performance-wise trading strategies end up in final ensembles. Using the Bitcoin market we show that the strategy ensembles outperform both in returns and risk-adjusted returns in the out-of-sample period. Even more so we demonstrate that there is a clear correlation between the success achieved in the past (if measured in our custom metric) and the future.

q-fin.TR↗