Philosophical and methodological aspects of predictive mathematical modeling are considered. Predictive mathematical modeling in the epoch of technological challenges to postindustrial society is becoming a third way of cognition, supplementing and uniting classical theory and natural experiment. The author describes conceptual, architectoral, and technological problems of creating an integrated software environment for high-performance solutions to interdisciplinary direct and reciprocal new-generation problems for multiprocessor petascale computing systems with scalable parallelism. Trends are unfolding in the development of “neoinformatics” with the introduction of cognitive principles into the automation of model and algorithm building and into the creation of decision-making systems for a wide range of users from various production and social spheres. Constructive and infrastructural principles are proposed for the development of an open basic modeling system that supports all basic stages of science-intensive computer experimentation and is oriented at an effective long-life cycle and coordinated development by various design teams.